The easiest solution to the Fermi paradox is that it is a selection effect: the ratio of time-to-conquer-everything to time-to-evolve-intelligence is rather small, with the addendum that going somewhere and not conquering it is pretty pointless. The ones who evolve first and go "But where is everyone?" then go out and control everything. And, maybe at some point, reflect back and go, "Oh, wait, huh, we stopped the chance of any others kinda by accident, didn't we?"

The second easiest is that the probability of evolving intelligent life per planet is far lower than one over the number of planets per galaxy, but far higher than one over the number of planets per universe, and galaxies are reeeeeeally far apart. That solves the "OMG how did we even happen" problem and the "but where is everyone" problem, and there are about nine orders of magnitude of room for that to be the answer. The problem then is where is the evidence for Kardashev Type III civilizations, because presumably those galaxies would look super-weird. The speed of light rescues some of that, though, and I don't think we've looked systematically anyway, have we (if we even knew what to look for)?