Fermi's Paradox was nonsense.
Fermi had much to offer as a physicist, but he had little grounding in alien intelligent life forms or interstellar astronomy.
There are many reasons why his so called paradox was flawed, and most of them are due to the fact that there is a tendency to attribute wisdom to learned people in one field to them in other fields they merely have opinions about. Some are due to human arrogance that thinks intelligent life would be necessarily interested in meeting us.
The fact that we don't see aliens here on a regular basis is due more to the vastness of space than to a necessary impossibility of them existing. If other planets have life forms capable of interstellar space travel, then they may have done so already. We are in a part of space with a relatively medium to low density of habitable planets. For us to travel to other stars would take several lifetimes, given that we had the technology to even try it.
I think it is worth keeping in mind that our Sun is in a relatively sparse patch of the galaxy. That's not to say that there aren't plenty of places where there are very much fewer stars than around here, but where there are no stars, we likely won't find any planets orbiting them, of course...
There are MANY regions vastly richer in stars than near here. What if there were a patch of space (and there are millions of such places in the galaxy) where the stars were far more densely packed? Intelligent life on any of them would have had a much easier opportunity to go visit other stars if there were several as close as a tenth of a light year or less away. It would be very possible that intelligent life had spread from planet to planet amongst many of the other stars. If each had planets (or even many) it would be easy to imagine that that within a relatively short distance there could be many habitable planets for them to choose from to visit.
I suspect first attempts at getting to any of them would be one way trips for the travelers. It could be conceivable that for any number of reasons the trip was rarely repeated, and the return trips were even more rare. After a few million years or less I would think the various life forms, sharing common origins, may have evolved in many different directions largely due to differences in the environments they had encountered and the events of their societies. That would be easy to imagine even if intelligent life only originated once on one planet. Suppose it happened on several all over a long time span. There could be quite unimaginable diversity if they started to encounter each other.
Consider them and us. They would be at least a few hundred light years away from us simply because the nearest such regions of space are at least that far away from us. Do you actually think they would bother looking further than their own neighbourhood for other intelligent life? Why would they bother? They may confidently assume that life is common throughout the galaxy and feel there were enough interesting species to communicate with (or avoid) without bothering to go much further.
Now let's back off and reverse it a bit. What if the normal distance between nearest stars in a particular region of space is several dozen light years? We haven't been able to confirm or rule out life on planets orbiting any of Alpha Centauri's stars, let alone planets there at all. What if any such stars had planets and intelligent life? We could have intelligent life on planets around all the stars within a 100 light years, and unless they were vastly more advanced than us, none of them would know, for sure, of the existence of the others.
If we then say that intelligent life is far rarer that that, maybe 1000 cases in the whole galaxy, that would leave us each a few hundred million stars to consider. I think Fermi was just a bit too impatient or arrogant in proposing his paradox...
If a very intelligent species existed out there somewhere, there is no reason to assume they would want to encounter the likes of us in the first place.