I'm not an astrophysicist, so somebody correct me if I'm wrong. My understanding is that due to the expansion of the universe, all the galaxies are moving away

I'm not an astrophysicist, so somebody correct me if I'm wrong. My understanding is that due to the expansion of the universe, all the galaxies are moving away from each other. The rate at which they move away from each other is directly proportional to the distance between them (the Hubble Constant), because space itself is expanding. Kind of like if you lined up a bunch of deflated balloons next to each other and inflated them at the same rate. At some point, around 13-15 billion light years away, galaxies are actually moving away from us faster than the speed of light. Also, because their "velocity" is proportional to the distance, they're actually accelerating away from us. With each year, more things reach a "velocity" where they're moving away from us faster than the speed of light, and will never be reachable without faster than light travel. Thus the Fermi Paradox only makes sense if you consider it likely that interstellar aliens could travel faster than the speed of light. If FTL travel is impossible, then a timer was started on the day the universe was created, counting down the seconds until our galaxies were moving away from each other too fast for contact to ever be possible. In that case, the Fermi Paradox is a paradox no more. It's entirely possible other life does exist, it's just physically impossible for us to contact each other.