The Talmud (Sanhedrin 97a) says, "The world will exist for 6,000 years, and in the 7,000th year, it will be destroyed." "Sefer Ha-Temunah", a first-century Kabbalistic book by Rabbi Nehumia ben Ha-Kanah, expresses the view - not universally held - that the 7,000 years of Sanhedrin 97a run parallel to the Jewish Sabbatical cycle, in which the fields are planted for six years and left unplanted in the seventh (Leviticus 25:4). After seven Sabbatical years comes the Jubilee year (every 50th year), whose laws are similar to those of the Sabbatical year (Leviticus 25:11). The 7,000 years are thus one Sabbatical cycle within the Jubilee cycle, and the universe must exist for a total of 49,000 years. (Yes, I know that's not 15 billion years. I'm getting to that.) There is a difference of opinion regarding which Sabbatical cycle we are currently in: Derush Ohr Ha-Hayim says that we are in the second cycle, whereas Livnat Ha-Sapir says we're in the seventh. According to these opinions, then, the world would have been, respectively, either 7,000 or 42,000 years old when Adam and Eve were created.
In the 13th century, Rabbi Isaac of Akko made the insight that, since Sabbatical cycles existed before man was created, time before Adam and Eve must be measured in divine years, not human years. Psalm 90:4 says, "For a thousand years in thy sight are but like yesterday when it is past, and like a watch in the night." Rabbi Isaac of Akko - who held like Livnat Ha-Sapir, that we are in the seventh Sabbatical cycle - therefore took the above figure of 42,000 years and multiplied it by 365,250 (he was using a 365.25-day year) to get 15,340,500,000 years for the age of the universe when Adam was created. This is roughly in line with what modern science is saying (15 billion years, give or take a couple billion), and Rabbi Isaac of Akko came up with it four centuries before the telescope was invented. (Today we know that there are 365.242199 days in a year. Thus, on the secular calendar, the leap year is withheld in years ending in 00, unless the year is also divisible by 400. Rabbi Isaac of Akko's calculation is thus refined to 15,340,172,358 years.)