But suppose they were around for only a couple of thousand years?!?!?
Nope.
As a Catholic priest, you might like to get into contact with Father Guiseppe Leonardi. His family have been scientists since the 15th century and the family home has the skeleton of a dwarf elephant on the third floor. That fossil is a million years old. He is a specialist in dinosaur tracks, and while studying for the clergy at Rome University, pursued a Ph.D. in paleontology.
Priest to priest, he may be able to better explain the geological study of stratigraphy in terms you could understand, and how it would be nigh impossible for fossils found on mountaintops to exist there after only two thousand years.