In reality, the universe that we can observe is expanding significantly faster than we can travel, even if we could go much faster than now.

Even if you imagine the universe is not infinite, it's functionally infinite from our perspective.

There are conflicting models of how we can have an infinite universe, that is also expanding (that bit always hurts my brain). So we don't know this for sure.

Essentially to quote the brilliant Douglas Murray "space is big. You just won't believe how vastly, hugely, mind boggingly big is. I mean, you may think it's a long way down the road to the chemists but that's peanuts to space"