I think there can be two approaches to the present question. One approach is of the scholarly type, attempting to nail down various corners of the flood story with the left brain, with logic, facts, reason, all in the service of incontrovertible findings - sort of like proving a theorem in geometry. This may be possible at some time in the future when more evidence is provided by anthropology, palentology, geology, and/or other branches of reductionist science. Right now, this proof via inference seems as good as we're likely to get using this approach.
Another approach is that of the right brain; of intuition, or perhaps just common sense. And I'd like to present some of that thinking now for your entertainment if nothing else.
Consider that at the time we're discussing, the population of the earth was very thin. Most civilizations, such as they were, were riverine. Now Noah, who had lived for a long time on the banks of his river, noticed that the level of the annual innundations fluctuated greatly. Sometimes the water went up very high; other times, not so high.
For whatever reason, Noah decided that all the signs and portents (and perhaps a whisper in his ear from Jehovah, weather god par excellence) indicated that in a few short seasons, the river was really going to come up very, very high - high enough in fact that his farm and his family were going to have a hard time surviving. (How long can you tread water?).
Having sufficient time to take preventative action if he started now, Noah proceeds to build a very large boat in which he can house his household, his animals, food enough for all for the relatively short while such will be required.
His neighbors, not exactly as prescient as Noah, make a joke out of him, but undaunted, he doggedly continues with his boat, ark, whatever.
When the time comes, Noah places his folks and his flocks and his foods on his boat, closes up the doors and sure enough, the annual innundation of the river this time is way, way higher than it had ever been. But Noah and his own are safe, snug, and fed in his boat while they wait for the river to recede. Of course, many of his neighbors drown in the flood (remember the Missouri/Mississippi flood of several years ago? And these people were protected by dykes, and all sorts of constructions by the U.S. Army Corp of Engineers (noticably lacking in Noah's time).
Well, the flood recedes, Noah's family, flock, and stuff are preserved and his wisdom is celebrated in song and legend for the remainder of life on this planet - at least by bible-believing, right-thinking, christians.
And any of you who have played "gossip," that game where twenty kids line up and a statement is passed from the first to the last child with the end result that the statement that comes out does not even resemble the statement that went in will recognize what happened next.
Noah's little feat of prescience was turned into an event of world-wide significance: a world-wide flood, complete with this one sage guy who was wise enough to keep an eye on the river stages all his life - since he lived right there on it.
But the story! Well, the story. Passed on from generation to generation. Generations that left the area eventually and spread all over the world, taking their oral histories of those times with them. Taking them, for instance, to the outback of Australia where there is a tradition, oral of course, of a world-wide flood.
And naturally, it's preserved in the Judeo-Christian tradition. And in all sorts of other places.
And it's really just a story of one guy who kept his eye out on the river he lived next to and did what any sane guy would do when he figured out that the river next year was really gonna come a frog strangler.
Now I know this story won't appeal too much to the left-brain types. Too simple. Makes too much sense. Doesn't require partial differential equations to solve.
Remember Occam?
Francois