> But infinite population growth is unsustainable

Only if we don't explore and colonize the stars. From what we know, the universe is infinite.

How many years/generations are you willing to spend on a ship in the middle of space? Remember, Biodome didn't work. Are you going to join that prison for the off chance of your progeny occupying a land that we haven't even discovered yet?

And, before you suggest it, no, there will never be faster-than-light travel, and even relativistic travel is super unlikely.