
This is an interesting question, as in the standard cosmological model (called ``$\Lambda$CDM'') our Universe is only about 13 billion years old and expected to exist and expand for a much longer (infinite?) amount of time. So the number of stars that are yet to be born is still large. Obviously, even in an eternal Universe the amount of gas available to form stars is limited. In an astrophysical sense, we recently passed the baby boom phase: The peak in star formation happened a few billion years ago, and the cold gas in galaxies is expected to be effectively exhausted in about 20-30 billion years or so from now. Long story short, it is possible to count how many stars have been born so far and what is their mass, and also how many more will be born in the future. Yes, astrophysics rocks!
