There were lots of shallow seas at various times. A lot of North America was under one, and among the remnants today is the Great Salt Lake. There are fossils of sea creatures in some of our vast desert regions in the West, and elsewhere. There were shallow seas and vast marshy areas covering a lot of the U.S.; wherever there were, you can find dinosaur tracks, coal and oil.
Continental crust is always on the move. Either the solid land under the polar ice caps was somewhere else warmer, on the planet long ago, and/or the atmosphere at some point was so thick with greenhouse gases that total global temperatures were high enough that there were global tropics and no ice even at the Arctic Circle.
You won't find land dwellers on the sea bottom because Earth is a water planet -- oceans are the constant, with land masses being either inundated by higher seas, or exposed to the air by lowering sea levels (during ice ages when much water is bound up as ice). The deepest reaches and trenches of the oceans were always such, and never were dry land, so there were never land plants or animals living there. The crust that was pushed up into the air and is now the Himalayas, was the bottom of shallow seas.
Another interesting thing going on 40 million years ago, and part of the same period of tectonic activity as the Indian subcontinent' collision with Eurasia, was the completion of the splitting of a mega-landmass into what are now South America and Africa. The plates beneath the mega-landmass were moving in opposite direction, sort of like someone on rollerskates having one skate go one way and the other skate going the other way...to perform an uninteneded split. If you look at those continents, you can see where they once fit together, and geologists have found the identical geologic formations and mineral contents on the east coast of S. America and W. Africa. Not only that, but the split caused a genetic drift in the species of animals living on the mega-landmass. The ancestor of the modern camelids had part of its population left in Africa and the other part separated by an increasingly growing distance of ocean. Today, we see the DNA connecting modern camels (Bactrian and Dromedary) of Africa and Asia (Asia having always been accessible to and from Africa) and the llamas, vicunas, alpacas and guanacos of S. America -- the result of genetic drift. Also, there are "Old World" and "New World" monkeys, parrots and countless other life forms, including now-extinct ones, that were similarly the result of the schism. South America has so many species of plants and animals with analogous African/Asian species, all resulting in the past 40 million years.