Well if we're going to ask for *evidence*.
Matthew puts Jesus' birth during the reign of Herod the Great.
Luke puts Jesus' birth during a Roman census held while Quirinius was Governor of Syria for the purpose of taxation, this happened after the Romans deposed Herod's son Herod Archelaus, in the tenth year of his reign (starting with the death of Herod the Great).
(See Josephus, _Antiquities of the Jews_ XVII.13 for the deposition of Archelaus and XVIII.1 for the census)
There is no evidence placing Qurinius as Governor of Syria prior to this (indeed we know that Quintilius Varus was Governor when Herod died and Saturninus before him), nor is there any evidence that a Roman census of Judaea for tax purposes was held prior to that - nor even a good reason to suppose that the Romans would hold such a census (Judaea under Herod paid tribute to Rome, a sum agreed between the Roman government and Herod so the Roman tax system did not apply).