I guess the difference between notional concepts and actual existents is a real evolutionary bummer.
Is existence finite or infinite?
Existence is not a thing, it is a quality. Everything that is has it. Everything that isn't, doesn't.
Sometimes "existence" is used to mean, "everything that exists." Every existent (thing) is finite.
Maybe your question is, "how many finite things are there?"
Sorry? I don't know; but I'm sure it's a finite number of things, but probably more than can ever be identified.
No actual existent of any kind can be infinite.
This automatically excludes the Gods of almost all religions which define their God as infinite, or eternal, or omniscient, or omnipresent, which are all kinds of infinities.
Hank