Hello Rudolf, thanks for taking the time to respond.

You asked:

"How do you know the universe is finite"

Everything we've ever measured about the universe is finite.

We know roughly when it began -- a finite number of billions of years in the past.

We know roughly how big it is, in terms of light-years across.

We know that the universe is expanding, and roughly the rate at which it is expanding.

We know roughly how many atoms exist in the universe.

All of these are finite quantities.