The Fermi paradox thing is nonsense in sci-fi, because you're not bound by it. You're specifically populating space with a lot of species.
But more importantly, it also ignores the more important statistical point: we might just be one of the first (and therefore the precursor) species to become space-faring. It took earth a long time to come up with us, and we might well **** it up before we get to the stars.
I've always found this particular explanation to be the weakest one for the Fermi Paradox, to be honest, because it reeks of anthropocentrism.
At first we thought earth was at the center of the universe because god made us oh so spechul, but then we discovered earth revolved around the sun. Clearly then, we said, surely the sun is the center of the universe because it would be absurd otherwise as we are the most important beings in existence. But then we discovered our sun was one of many, and our galaxy one of many, in perhaps even a universe that is one of many. And worse still, that we were not divinely created, but merely an animal variant, a member of the Great Apes
For some, I think such anthropocentric ideals now induce a crisis of existence. We look to the stars for others like us, we listen and send out messages and we receive silence in response. We make statistical models on the likelihood of intelligent life, and mathematical models on how easy it would be to spread across the galaxy at sublightspeed. And then we say "well, clearly it is a paradox....unless WE are just so spechul that we are teh first! Yay us! Go humans."
But really, it is just a restatement of anthropocentrism. Just like helio and geocentrism before, we KNOW we are insignificant in the greater scheme of the universe but we just dont like to accept that. There are planets in the Milky Way that have been around for over twice as long as the Earth, mostly in red dwarf systems. There is ample opportunity for intelligent species to be billions of years more advanced than us. And yet we think WE are the first? Honestly, the idea makes me chuckle a little bit. Hopefully that brief history of scientific exposition of our place in nature makes you see why.
So no, I highly, highly, highly doubt that we are the first. And while self-extinction events are probably more common than not, it only takes one species to spread out to the stars to completely colonize the galaxy within fifty million years. Personally, I suspect that the answer to the Fermi paradox is either that we lack the means to detect them and they don't care about us, or that most civilizations are post-organic or synthetic.