This one says it is
I am not sure whether to ask this in geology or biology.
How does marine fossils show up in mountains?
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Leonardo was wrong about this. It is not due to sea level dropping (except in very isolated cases), it's due to the land rising. Sedimentary rocks that form in sea beds are often uplifted by tectonic processes to form mountains and plateaus. See e.g. https://en.wikipedia.org/wiki/Sedimentary_rock
Note that this answer was given when this question was on biology.stackexchange.com. @jamesqf has IMO a better, more informed, more helpful answer below. I don't pretend to know much of anything about geology!
I'd say that Geology is the better venue, but nonetheless here is an answer.
Note that there are lots of reasons why elevation changes in geology. The structure of the Earth's crust is itself constantly in motion, such that new plateaus and mountains can be "born" from the sea's floor and thrown up by volcanism, temperature changes, plate friction, etc.
This seems to be pretty old work in geology, see e.g. here.