There is no reason to think that the stories were not written down immediately near the events. After all, these were literate people. The archeology of the regions reveals all kinds of writings, methods, transcriptions, scribes, etc.
And since prophecy was guided by a prophetically active God, He made sure that what did get written down was right. So even if the story had lived on to that time only orally and had gotten cockeyed, the biblical inspiration would not be wrong. That would be like hearing a rumor than having someone who was in on the original event tell you exactly what happened.
>There is no reason to think that the stories were not written down immediately near the events. After all, these were literate people. The archeology of the regions reveals all kinds of writings, methods, transcriptions, scribes, etc.
Look to your earliest Garden of Eden stories. There was no writing communication for thousands of years after these events.
Elementary pictographic "writing" by a few professional scribes by the time of the Exodus, certainly, but much earlier than that, no.