How do we know when the Gospels were written?

The Four Gospels were not known to the early Christian Fathers. Justin Martyr, the most eminent of the early Fathers, wrote about the middle of the second century. His writings in proof of the divinity of Christ demanded the use of these Gospels had they existed in his time. He makes more than three hundred quotations from the books of the Old Testament, and nearly one hundred from the Apocryphal books of the New Testament; but none from the Four Gospels. The Rev. Dr. Giles says: "The very names of the Evangelists, Matthew, Mark, Luke, and John, are never mentioned by him [Justin] -- do not occur once in all his writings" (Christian Records, p. 71)
There are many extant writings accredited to the Apostolic Fathers, Clement of Rome, Barnabas, Hermas, Ignatius, and Polycarp. These writings contain no mention of the Four Gospels. This also is admitted by Christian scholars. Dr. Dodwell says: "We have at this day certain most authentic ecclesiastical writers of the times, as Clemens Romanus, Barnabas, Hermas, Ignatius, and Polycarp, who wrote in the order wherein I have named them, and after all the writers of the New Testament. But in Hermas you will not find one passage or any mention of the New Testament, nor in all the rest is any one of the Evangelists named" (Dissertations upon Irenaeus).Tlosophy.
It has been written that never has a book been read so often but examined so infrequently. Many like to say that the four Gospels were written around`70 Ad. Gospel of the Nazoreans was quoted by Ignatious in 98 A.D. and so was written prior to this date and was associated with the early Nazoreans. The Stichometry of Nicephorus assigns it 2,200 lines, 300 less than Matthew. (this may not have been the original Gospel of the Nazoreans however). Various old references to the Nazorean/Hebrew Gospel sometimes lead researches to think that there were four different Gospels but it is more likely that one document was the source of a score of others
"Is it possible seriously to maintain that there were two separate documents, each of them written at Jerusalem during the Apostolic age and in the Hebrew tongue, each of them assigned to the Apostle Matthew, and each of them dealing in some way with the Gospel story? Or are we not rather forced to the conclusion that these two documents, whose descriptions are so strangely similar, must really be identical,..". (A. S. Barnes; the Gospel according to the Hebrews; Journal of Theological Studies 6 (1905) p. 361
LITERARY DNA TEST ALSO SUPPORTS THE ONE DOCUMENT Theory. Open-minded biblical scholars in today’s world continue to seek for the ancient “Q Document” of Christianity’s New Testament. The Q Document is known by biblical scholars to be the source of the Bible’s New Testament. True biblical scholars, who have devoted their lives to studying the Bible with an open mind, concluded long ago, that the descriptions of Jesus’ life and teachings by Matthew, Mark, Luke and John were so similar, that there had to be one source document that was used to “write” their “Gospels”. Biblical scholars have for years called this missing link to the New Testament, the “Q Document”.
The “Q Document” was used by the Roman Emperor Constantine to devise his Roman Universal Church. The Q Document was decreed by Constantine to be the document from which 4th century Roman writers would write the Gospels of the New Testament, accredited to Matthew, Mark, Luke and John. Only those sayings and teachings of Jesus, specifically approved by Emperor Constantine, were included in the “Q Document” and the New Testament of today’s Bible.
The Q Document did contain some truths of Jesus’ life, but it was specifically written with many untruths, omissions and deliberate mistranslations. Even worse, the words of Saul/Paul were used extensively in Constantine’s New Testament. Saul/Paul never met Jesus in person. Saul/Paul’s only experience with Jesus was when Saul/Paul had a vision over his persecution of those individuals who were following Jesus’ liberal philosophy and performing Jesus’ spiritual techniques.“Early church father Eusebius, who, in a rare moment of seeming honesty, "admitted...that the canonical Christian gospels and epistles were the ancient writings of the Essenes reproduced in the name of Jesus.Well known biblical scholar Taylor also opines that "the travelling Egyptian Therapeuts brought the whole story from India to their monasteries in Egypt, where, some time after the commencement of the Roman monarchy, it was transmuted in Christianity." In addition, Wheless evinces that one can find much of the fable of "Jesus Christ" in the Book of Enoch, which predated the supposed advent of the Jewish master by hundreds of years. According to Massey, it was the "pagan" Gnostics--who included members of the, Essene/Therapeut and Nazarene brotherhoods among others--who actually carried to Rome the esoteric (gnostic) texts containing the Mythos, upon which the numerous gospels, including the canonical four, were based. Wheless says, "Obviously, the Gospels and other New Testament booklets, written in Greek and quoting 300 times the Greek Septuagint, and several Greek Pagan authors, as Aratus, and Cleanthes, were written, not by illiterate Jewish peasants, but by Greek-speaking ex-Pagan Fathers and priests far from the Holy Land of the Jews." Mead averred, "We thus conclude that the autographs of our four Gospels were most probably written in Egypt, in the reign of Hadrian." .
Rene Descartes once said that if you begin with doubt you will end with certainties.and if you begin with certainties you will end in doubt. I read this years ago and thought the whole concept preposterous and foolish. Now, I believe it to be more than just a theory since the most recent gospels were discovered in Egypt and many feel that the Gospel of the Essenes were the original “Q” Testament in which the four gospels were derived.The Roman Church created a history of the triumph over Essenic Apostle Christianity in much the same partisan way that, two millennia later, Hollywood created
Tales of “cowboys and Indians” to relate “how the West was won” not “how
The West was lost.” History is not simply related, it is created . All too often . it
Is simply [used] to glorify and justify the status quo. Such histories conceal
As much as they reveal.And so it was that the Roman Emperor Constantine devised a male-dominated religion, which he called the Roman Universal Church, using fear to control people and giving people only the weakest portions of Jesus’ spiritual teachings. In this manner, the God-loving philosophy of Jesus, together with his spiritual wisdom and energetic techniques for Enlightenment, were deliberately weakened, or completely omitted from the New Testament, so Rome could continue its economic control of the world using the God-fearing philosophy of the Roman Empire’s Universal Church.
And so it was that many devious methods were used by the Roman Empire’s Universal Church to greatly modify and lessen the wonder-filled life history of the man who became a Christ. In this way, most of Jesus’ life, (called the missing years), were omitted from the Roman Empire Church’s New Testament. Christianity has been so spiritually weakened in today’s world that only one or two people, (out of 2 billion “Christians”), in a generation are able to attain Enlightenment in their lifetime. Yet, as seen in ancient paintings, using Jesus’ true teachings and techniques, most of his disciples and students, reached Enlightenment in that one lifetime.A contemporary said: We have proved again and again, the writings are not the production of Christ or of His apostles, but a compilation of rumors and beliefs, made, long after their departure, by some obscure semi-Jews, not in harmony even with one another, and published by them under the name of the apostles, or of those considered the followers of the apostles, so as to give the appearance of apostolic authority to all these blunders and falsehoods." (Faustus, Contra Faustu

Your problem is you are trying to use the Bible to support an argument.Studing falsehoods with great intensity seldom will seldom increase knowledge. I study all the Gospels. When in doubt on an issue I go to the Gospel of the Essenes. I also study the early Christian known as "the followers of the way" (the Ebionites) I can assure you nothing I have written is fabricated. Before you quote Paul, I recommend you research a little of his background. He deified the death of Christ and not his teachings..The Truth frees all of us to finally admit that somehow, some way, we just knew there was something wrong with what we'd been told to believe without question. The Creator gave us brains -- and minds with which to explore the mysteries of this wondrous universe. We can never learn new truths if we have a mind cluttered with preconceived opinions because blind faith stifles curiosity, and without curiosity, there can be no great discoveries. Blind unquestioning faith is the prison door that Jesus came to throw open. It was the superstitions keeping people oppressed that he sought to destroy. He had discovered the Truth, and the Source of the Truth. He had found Moses' secret doctrine and the glorious knowledge it contained. He wanted to share that knowledge with the world, even if it might cost him his life to do so. He knew that knowledge is Power. Always question those who say they have found the truth, more readily than those who say they are seekers of the truth.

St. Irenaeus wrote:"It is not possible that the gospels be either more or fewer than they are. For since there are four zones of the world in which we live, and four principle winds, while the Church is scattered throughout the world and the pillar and ground of the Church is the gospel, it is fitting that we should have four pillars breathing out immortality on every side" (Catholic Encyclopedia vol. VI, pg. 659).As for the writings of Paul, the Encyclopedia Biblica states categorically:"With respect to the Canonical Pauline Epistles, none of them are by Paul. They are all, without distinction, pseudographia (false writings). The group (ten epistles) bears obvious marks of a certain unity, of having originated in one circle, at one time, in one environment, but not of unity of authorship" (Encyclopedia Biblica III pg. 3625-26).The Father of Christianity appears to be Paul and the Father of the history of the Christian Church appears to be Eusebius. Both never knew or walked with Jesus. Yet, Christians today believe everything these two men want them to believe. Christians believe every word they read and hear to be the words from God.Most of my references come from scholars and historians. I long ago realized that that a seeker of the truth cannot rely on doctrines or dogmas. Those who rely on doctrines will readily quote from scriptures to prove a point. What we are trying to do is penetrate the mysteries behind the scriptures. There lies the real truth. and yet many betting their souls on man-made words. How sad!I recommend you start by reading Origen, philo of Alexandria; then follow the pathway of the Gnostics, Essenes and maybe the "poor ones" The Ebionites. In your studies remember--very little is pure truth, but what we have is evidence and you will need knowledge to sort through the mountains of trash to reveal a few golden nuggets of truth

Here is some more material that might help you. Again, wll we have is evidence and not proof.Forgeries were so prevalent two thousand years ago that one does not know what to believe. I have been trying to answer the question Paul" Apostate or Apostle" and most evidence seem to indicate apostate. Jesus died for your sins.A missionary preaches in India that the New Testament is the revealed scripture, or word of God. The educated Hindus, however ,knows that of the fourteen epistles attributed to Paul, four only are held to be authentic; they are these: Epistle to the Romans, First and Second Epistles to the Corinthians, and the Epistle to the Galatians.
Scholars point to the “Acts of the Apostles” as definitive proof of forgeries deletions and Biblical insertions by the Roman Empires to combat what they considered heresies of the Gnostics.
”Another scholar wrote the following about the acts:” Acts of the Apostles was written (150-177 CE) to account for his disciples. It reads like a fantasy novel, misquotes the Old Testament, and contradicts Paul's letters. It is now acknowledged to be largely if not entirely a fabricated picture of Christian origins designed to serve the purposes of the Roman Church. Finally, the Letters of the Apostles were written (177-220 CE). Modern scholars have shown that the letters ascribed to Peter, James and John are forgeries written much later to combat heretical (Gnostic) ideas within the early church; they attack 'many deceivers' who 'will not acknowledge the coming of Jesus Christ in the flesh' (2 John 7). Paul's early (and mostly genuine) letters are full of Gnostic phrases and teachings, whereas his later letters (the Pastorals) are anti-Gnostic, If Paul’s teachings were Gnostic and the fakes were anti Gnostic maybe the condemnation should be solely on the Roman Universal Church and not all Paul because these letters are regarded as fakes by all but the most conservative of theologians. Forgery during the first few centuries of the church's existence was so rampant that the phrase 'pious fraud' was coined to describe it. “
One story in the acts involves Paul and an Essene called Simon Magus. Paul thought he could buy spiritual powers from Peter and was rebuked; later this story was revised to show the seeker of spiritual power was Simon Magus. All these falsities to combat the teachings of Christ which was Gnostic and Essenes build on spiritual ideas and not pure faith. This information was from Ebionite scripture that pre-dates the acts so once again it is a matter of whom do you believe, the Romans or the Ebionites. We have historical evidence but no conclusive proof; again the original tale was part of the Ebionite scriptures and the revision was anti Gnostic and a probable fabrication of the Catholic Church.
"Paul was the first corrupter of the doctrines of Jesus!"
-- Thomas Jefferson
Paulinism overran the whole western civilized world, which was at that time the Roman Empire, and was adopted by it as its official faith."
Mark Twain once stated that Paul was the one who created all the problems. We know the Essenes also referred to him as the first corrupter of the teachings of Christ
Unfortunately some our greatest leaders and minds have had to look elsewhere for spiritual growth .Just to name a few from a very long list Emerson, Thomas Jefferson, Lincoln, Mark twain and even Benjamin Franklyn are just a few that didn’t care for Paul and the Constantine scriptures I have always respected the opinion of Thomas Jefferson. Abraham Lincoln, Mark Twain, Waldo Emerson, Henry David Thoreau is some that also share the opinion of Jefferson.
There are many, many more that had a negative opinion of Paul and all were scholars. MY favorites were Thomas Jefferson and Gandhi
Thomas Jefferson's Opinion of the four gospels - 1814
"The whole history of these books is so defective and doubtful that it seems vain to attempt minute inquiry into it: and such tricks have been played with their text and with the texts of other books relating to them, that we have a right, from that cause, to entertain much doubt what parts of them, form that cause, to entertain much doubt what parts of them are genuine. In the New Testament there is internal evidence that parts of it have proceeded from an extraordinary man; and that other parts are of the fabric of very inferior minds. It is as easy to separate those parts, as to pick out diamonds from dunghills. The matter of the first was such as would be preserved in the memory of the hearers, and handed on by tradition for a long time: the latter such stuff as might be gathered up, for imbedding it, anywhere, and at any time"(Thomas Jefferson - 1814)
The brilliant theologian Ernest Renan, in his book Saint Paul, wrote: "True Christianity, which will last forever, comes from the gospel words of Christ not from the epistles of Paul. The writings of Paul have been a danger and a hidden rock. The causes of the principal defects of Christian theology."
Albert Schweitzer, winner of the 1952 Nobel Peace Prize, has been called "one of the greatest Christians of his time." He was a philosopher, physician, musician, clergyman, missionary, and theologian. In his The Quest for the Historical Jesus and his Mysticism of Paul he writes: "Paul....did not desire to know Christ....Paul shows us with what complete indifference the earthly life of Jesus was regarded....What is the significance for our faith and for our religious life, the fact that the Gospel of Paul is different from the Gospel of Jesus?....The attitude which Paul himself takes up towards the Gospel of Jesus is that he does not repeat it in the words of Jesus, and does not appeal to its authority....The fateful thing is that the Greek, the Catholic, and the Protestant theologies all contain the Gospel of Paul in a form which does not continue the Gospel of Jesus, but displaces it."