Another answer to the Fermi paradox is that a Kardashev Type 4 civilization is able to harness the power of an entire universe. We wouldn't be able to detect this by definition, since they exist outside of our perceived reality.
At first glance, this seems to be a useless theory, since it's not refutable. But it lends itself to a belief system: by studying the universe, we gain an understanding of whatever created it. This is helpful as a motive: a reason for studying any of this at all, in absence of economic or social incentives.
This seems important. As the centuries tick by, and as we confirm and re-confirm that we are indeed alone and that we do indeed have a mostly-complete model of physics, there will become less and less incentive to analyze the corner cases. It's costly, and takes decades. But at one time, it was costly and took decades to build a cathedral. Yet we accomplished these impressive feats due to a shared belief system.
The reason I brought this up is that we often like to believe there is an advanced alien civilization tucked away in some corner of some galaxy, sending out messages via gravitational waves or neutrinos. But why do humans find this idea so seductive? It's because of an underlying loneliness: we want to believe that we are connected with the universe in some fashion, that our existence has a point, and that there is reason to do anything at all in a universe that will exist long after we've gone, long after our solar system and sun has gone. Because if there were an alien civilization, at least we would not be so alone.
In that context, a solution to Fermi's paradox is simply to believe that our very universe exists due to some higher-order phenomena not knowable within our reality. And by studying the laws of physics, we gain a glimpse into the boundary between our universe and its hypervisor.