In my humble opinion, time is finite.
After all, if we assume time is infinite, then there must have been a physical event in the infinite past. But if it happened an infinite time ago, time should never have reached today.
A more formal way to write this argument is:
A moment is the shortest time in which a movement of any (real) material object could be observed by us humans.
A. An infinite number of moments can never conclude. (There can always be one more moment in an endless series)
B. If there were an infinite number of moments before today, then today would have never arrived. For the present moment would be the one that concludes this infinite series of moments.
C. But today has arrived.
D. Therefore, there were only a finite number of moments before today. (Thus the universe had a beginning).
This argument was first proposed by St. Anselm hundreds of years ago.