People like Ray Kurzweil, Jürgen Schmidhuber, Leopold Aschenbrenner, Paul Christiano see a pathway out of this inevitability through technological singularity. In their vision humans are a seed to something greater, something noticeable on cosmic scales. In their vision, like early humans who emerged on the other end of genetic bottlenecks, today's humans will have a disproportionate effect on the future. According to the current models of cosmology heat death of universe in still inevitability but that's on a completely different timescale than human life.
Please don't take this to be dismissive of your comment, because that's not my intention, but...
I think people like Ray Kurzweil are essentially religious. Instead of a messiah and heaven, they think of salvation in terms of a singularity, immortality, or a way of ascension. It feels very religious to me, and as such, detached from reality and physical possibilities.
Yeah. He makes a good case for the computer side of upload being possible--and totally skips over the biological side, assuming it will be available on the same time frame.
Even if upload does not produce a singularity or the like it still is a huge step towards getting more time to address other issues and it makes interstellar solutions viable. But when we can read out the human mind remains an unknown.