From what I understand, there was a near-mass extinction, only about 75,000 years ago (if you go with the Toba super-volcano eruption being the cause) and with several thousand humans surviving.
It would not surprise me if the story of Noah and similar stories to that in almost every mythology is an long-remembered account of that disaster. Considering the massive geologic dislocation and the impact on the weather, it would have seemed that the whole world was suffering a great disaster. Indeed, their entire world was, most likely blotted out.
There are lots of volcanoes an floods, earthquakes and hurricanes. In central America they even have a word for jaguars falling out of the sky. All this centuries before the NFL.
With things like this happening in an average person's lifetime, why do we need to suppose that cultural memories are likely to be passed on for tens of thousands of years.