I always found the Fermi paradox too non-paradoxical.
If the closest aliens are in Andromeda, we can't pick out their radio signals, and we might never be able to. Yet it would still mean there are an insane number of alien civilizations in the universe, counting in hundreds of billions. So even if the universe is teeming with life, they could still be so far away that we would never be able to talk to them.
Yeah, pretty much this. The universe is big. Distance between habitable worlds is likely huge as well. Given the tendency of life to survive in the craziest places on Earth, I have little doubt it exists in some form elsewhere. But intelligent life existing close enough to Earth to encounter it is considerably less probable.