How do we know this?
If you won't accept any other evidence, consider continental drift.
From the locations where T. Rex and other dinosaurs were found, either they were adapted to colder climates, or the continents drifted tectonically to reach their present locations carrying the bones of the dinosaurs.
It takes a lot of time to move a continent. Heck, I'd have trouble pushing a Continental more than a couple of blocks.
Uhh...Cause our ancestors would have been eaten if they existed at the same time as them.