Yes, we’ve proven that pi is an irrational number and therefore has infinitely many digits.
if you picked one digit as the “last” one to start with, then you could express it as an integer faction and it wouldn’t be irrational. So that can’t happen.
You can express pi in irrational bases like base pi or tau, and then you have a finite number of digits (1), but that’s just putting a trench coat on top of pi and pretending it’s finite length so you can get into the movies. I don’t even know what you’d call those digits. But they wouldn’t let pi into the airport or courthouse like that.