the universe is finite to our reach and especially to our time

Some of the smartest people alive don't think so...

Big Bangs can be sequential, an endless cycle. Even in a "heat death" there's still black holes that over trillions and trillions of years will keep slowly getting closer to each other until eventually they combine.

The real heat death of the universe is one super massive black hole, and on a long enough timeline something will eventually happen which makes it spit all that matter and energy back out. Or even weirder, the inside is the new universe likely with random ass physics.

Like I said, the monkeys arent literal. It's a way to explain that infinite means everything