Infinite and “finite but very very big” seem like a meaningful distinction here.
I once wondered if digital intelligences might be possible but would require an entire planet’s precious metals and require whole stars to power. That is: the “finite but very very big” case.
But I think your idea is constrained to if we wanted a digital computer, is it not? Humans can make intelligent life by accident. Surely we could hypothetically construct our own biological computer (or borrow one…) and make it more ideal for digital interface?