Geneticists can use molecular clocks to calculate how far back in time different species diverged from their common ancestors, and it's clear that there was no global genetic bottle-necking event such as that described in the story of Noah's Ark.
Paleontologists can track the systematic morphological changes of virtually every clade of organisms, including ourselves, over 300 million years back, and the changes represented in the fossil record are identical to those represented in both embryonic development and in the molecular clocks mentions above.
Archaeologists and anthropologists have a continuous record of multiple cultures throughout the world and there was no point in time at which all of them were simultaneously flooded, nor do any of them outside of the Mediterranean region share an analogous flood myth.
Speaking to the flooding event itself, geologists are in agreement that sea water from the Mediterranean breached its sill and spilled into the Black Sea via the Bosporus Strait, resulting in a sea level rise of up to 30 meters, dramatically increasing the Black Sea's coastline. This occurred between 7,600 and 9,400 years ago, which roughly matches the hypothesized origin of the Deluge Myth.