What are you talking about? How can we possibly use up the universe?
By geometric expansion of our domain, once we escape from being constrained to this one mudball we currently occupy.
A McDonald's in every cubic nanometer--that's our motto.
Go back and read the argument: It wasn't my suggestion. I think our DNA will discorporate through rampant speciation into various channels that no longer support brains that can maintain a space-faring technical culture, long before we can get to even a tiny fraction of the universe.