Oh, there were lots of floods, local floods, all over the world.
But global flooding (of such a magnitude that, for example, the Greenland ice sheet would have floated away) would have left all kinds of markers in the geological record: tree rings, layers of sediment, ice cores etc. that are simply not there.
How could the Greenland ice sheet develop in only a few thousand years, many more than three or four thousand annual ice layers are found in ice cores.
A geological record of many strata, of varying types including both sedimentary and igneous layers is far better explained by multiple different processes over the ages than by one catastrophic flood event.
For your flood to produce the layers we see would require a miracle. Not just the layers of lava, but the problems with the locations of fossils. Larger, denser fossils would be found at lower levels, smaller, lighter at higher levels. Unless the waters were extremely turbulent, but then we'd see everything mixed together, humans with trilobites and dinosaurs with wolves, etc.
Then there's the problem of how it all turned from mud and carcasses to shale, sandstone, limestone, etc. in only a few thousand years.
If you drop a rock you will hear a sound. If you drop a larger rock, you will hear a louder sound. If you drop a rock millions of times bigger, you will get a much much louder sound.
Geologists have seen the results of floods, and from that we have ideas about what would allegedly happen in a flood millions of times bigger. But what you say about how this flood behaved is so completely different (layering sediments, etc.) it's as if you were claiming that the rock millions of times bigger would actually be more quiet than the smaller rock!
Sometimes somebody does come along and overturn the established wisdom.
In this case the "established wisdom" was the legend of the great Flood.
The people who came along and overturned that established wisdom were the natural philosophers, geologists, paleontologists, chemists, physicists, etc etc etc, who showed that the Flood could not have been anything but a local event, if it even was a particular event and not merely a memory of various floods over the ages. "Speak to the Earth and it shall teach thee."
But if you agree that fossils did fossilize, as you seem to, and you agree that it takes a long time for a fossil to fossilize, to say nothing of such processes as clay becoming shale and then becoming slate, how can you think the mud and carcasses of the flood could become the geological strata we see now in only a few thousand years?
But what you're describing is far more likely in a quiet little backwater with a lot of time for dirt and sand and debris and fossils to settle out slowly than in the aftermath of a catastrophic world-scouring maelstrom.
Zeus, Thor, Indra, etc. Why should different cultures all have a thunderbolt-throwing god?
Big floods are life-changing events, from Johnstown to the great Mississippi flood of 1927 to Katrina. They go back far into history: the Nile floods, the monsoons in south Asia, the tsunamis of the Pacific ring of fire, the Lake Geneva flood of the year 563, the Yellow River is known as "China's Sorrow" for the catastrophic floods that killed millions and scoured the countryside, changing the very landscape. Water is life and people live near water.
The floods of the Yellow River or the Nile floods or any other catastrophic event would have come down in history as affecting "everyone" and "everything" because they affected all the world known to those people.
The bible doesn't refer to China, so why should a flood referred to in the bible be thought of as affecting China?
The bible literalists would say that a flood referred to as covering all the world meant a flood covering the entire surface of the planet simultaneously, rather than just the part of the world the storytellers knew. But the bible is clearly not to be taken literally (There obviously were rainbows before the time of Noah, for example).
The fact that you use "backwater" without thinking it strange indicates how familiar people are with water!
People living near water (which is a lot of people throughout history) would have often been subject to floods. Some they would have stronger memories of (just as the 1927 Mississippi floods come down to us through history). They would form the basis of a myth.
Or maybe someone just made up the story, needing some catastrophe familiar to their audience to fit into a narrative of their god scouring the unclean and sinful from the face of the earth. They might have used an earthquake or a pestilence just as easily.