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No idea what Jewish literacy was like at the time, but I do know that there's a difference between the Oral traditions of the Talmud/Midrash, and the Torah itself, which was read to congregants by the Kohen Gadol. So even if literacy was a Rabbinical priviledge, the Torah was still kept through a literary tradition. By the time the Torah was translated to Greek it was seen as an offense akin to the Golden Calf, because it was believed a translation was impossible. I believe the Torah as one compiled book is credited to Ezra the Scribe around 400 BCE -348 BCE.