You mean besides because it wasn't practical. When exactly do you think the widespread dissemination of written materials occurred?I don't see why they wouldn't write it down.
Any time there was famine and drought people in surrounding areas headed for the Nile Delta... so that much is probably true. Otherwise the story is pretty fantastic and full of anachronisms. Taken as a foundational myth or a morality tale of redemption it makes sense.
Which story? Exodus?