Putting aside the more exotic possible configurations of matter that might be capable of self-replicating, computing, and having qualitative experience, but that we likely would not recognize as life, limiting the possibilities just to recognizable organic matter that depends upon carbon and water, I still expect life to be all over the place. If it's possible at all, which we clearly demonstrate by our existence, then it's inevitable, given enough space and enough time and enough chances.

I don't see any paradox in the Fermi paradox, though. The universe is just a very big place. Estimates currently seem to place the number of galaxies in the observable universe roughly within the same order of magnitude as stars in the Milky Way. Most of these are far enough away that we only see them as they were billions of years ago. Organic life can only develop in second-generation stars, because carbon and oxygen won't exist until then, not to mention all of the elements making up rock necessary to form terrestrial planets. So the chances of seeing organic life that far away is close to nil.

So that leaves other galaxies in the local supercluster, but life detectable from a distance would still have needed to develop tens to hundreds of millions of years earlier than us to be detectable now. Certainly not impossible, but constrained, and even if they colonized their own galaxy, if that's a different galaxy, that doesn't mean we'd see it.

So what about the Milky Way itself? Well, what if organic life that develops intelligence, civilization, and technology is simply rare enough that you maybe get one or two per galaxy. That would still be incredibly common across the entire universe, but low enough density to be entirely reasonable that you'd be very likely to never see it. Why would it be that rare? I think we underestimate a bit how lucky we got. Many systems similar to ours have a hot Jupiter, which makes it impossible for the inner planets because they effectively experience a permanent late heavy bombardment. On the other hand, the fact we had a late heavy bombardment at all may be a reason we have as much water as we have, but we needed Saturn to be in the position it is in to stop and reverse the inflow of Jupiter's orbit to eventually calm things down.

Then we got life, but for a very long time, it only progressed in the direction of the red queen race of the dinosaurs becoming ever bigger and stronger and more heavily armored. In some cases, also more intelligent, but it's unlikely the competitive constraints they faced would ever have allowed for a dinosaur civilization to emerge. Some paleontologists have speculated Troodon may have had a chance, but it's hard to say. I think we can say with some confidence that live birth and maternal nursing played a large role in the development of strong social behaviors and persistent communities seen in mammals but largely not seen in other animals. How likely was this specific adaptation to occur? Is it inevitable that it occurs first in smaller, nocturnal, underground creatures that raise their young in dens with minimal resource requirements? If so, then you also need something like a K-Pg extinction event that eliminates the brutes but leaves behind the little guys living underground to come out and take over.

All in all, maybe this is the case, maybe this isn't, but all it takes is a few tiny adjustments to parameters to the Drake equation and you get a very low density of life, but as long as that density isn't zero, the universe overall would still have lots of life, but nonetheless lots of life we're very unlikely to ever see. We don't even know the actual bounds of the universe. Outside of past light cone, it may be twice what we can see, it may be hundreds of billions of times what we can see, it may be infinite. Space and worlds we will never see no matter how long we exist and what technology we develop, but even if it's only one civilization per 14 billion year light cone, that may still be a very large or even infinite number.