Another way of phrasing the facts is that on every planet we know of where life has evolved, intelligence has also.

over 3.6 billion years, across 50 billion species, earth has produced exactly 1 sapient species.

I think this is somewhat debatable. Whales and dolphins are rather intelligent, as are apes and some other creatures. They are not human level intelligent, true. However, I do not think they are horribly far away from human intelligence. I would not be willing to assign less than a one in ten thousand chance to the possibility whales, apes, or dolphins would have naturally evolved to reach human level intelligence; given the size of the universe this seems like a high enough chance that we should expect intelligent life to be out there.

You mention that Earth has existed 3.6 billion years, but those are a pittance on the astronomical time scales we're dealing with. My large numbers eat yours. The fact it only took 3.6 billion years for Earth to produce intelligence is actually a strong point in favor of my position.

Unless you're superstitious, life can only exist within conditions that allow chemical reactions to take place. This qualification alone eliminates the overwhelmingly vast majority of space within the universe.

This eliminates a lot of space. But I don't know if it eliminates an overwhelmingly vast amount. Not enough to get rid of the paradox on its own. Theories that say human existence is essentially impossible are less well suited to the evidence than theories that say the existence of sentients has a small but definitively nonzero probability.

Our observations are pretty narrow. We've observed one planet up close for a couple millennia, and have had a decent view of a few thousands more for less than a century. With the amount of space we're dealing with, it's almost impossible to sufficiently stress how relatively small and shallow those observations are. We've looked at less than half a fraction of epsilon. Actually, less than that amount half again.

It's hugely more likely that advanced civilizations never have the chance to evolve in the first place due to catastrophic events which regularly wipe out the possibility of all organic chemistry.

I agree that uncountably many advanced civilizations never come into existence, of course. But I think it's likely enough of them have come into existence that further explanations are called for to help us to deal with Fermi's paradox.