He does not posit that "no communications took place".
If you want to argue that there was literature before what is generally accepted as "first literature", or writings before "first writings", but traces have been erased, then you'll have to go argue with someone else than Jaynes first.
If you want to argue that there was literature before what is generally accepted as "first literature", or writings before "first writings", but traces have been erased, then you'll have to go argue with someone else than Jaynes first.