Does the whosoever in John 3:16 indicate that salvation is not provided for just a finite amount of people, but rather to all?

The latter part of John 3:16 reads "whosoever believeth in him should not perish but have everlasting life."

But, would you not agree that this is talking about the condition to inherit eternal life? In other words "everyone believing in the Son has eternal life?"

The "whosoever" cannot be removed from "believeth"; it's not a general "anyone can", or "anyone who wills", but a "whosoever believeth."  The condition for eternal life is belief.

Other verses must be looked at to determine the nature or origin of belief.  Does it come from the person and is everyone capable of it? This verse doesn't tell us if belief is something that anyone can do, but just those who have belief have eternal life.