Well you say, "needed" which is an interesting choice of words. Not sure I get the argument your'e making. You don't think they needed to write. So, after the flood they did need to write?
Right, just as before Babel, no one needed to learn other languages. Something changed.
They say Babel happened when Peleg was about 5 or 6 years old. It was in the days of Peleg that the earth was divided also. I also deduce that it is likely that nature changed in those days.
After the change, we see hieroglyphics and such come to be used. It was at that time that Greece, and Egypt and I think it was Assyria became nations. All within several decades. I assume writing followed, as the word picture communication improved etc.
And now you're saying Moses didn't write Genesis as one account? Rather he wrote several books?
No.
I am questioning some other book you claim existed apparently. When I read Genesis mentioning that what follows is the book of generations of Adam, I take that to mean something like
'Here comes the part of Genesis where we record the sons and years etc' not 'here is some reference to some mysterious book that was used to write Genesis'