The Fermi Paradox is rooted in the idea that if alien intelligences were doing things that we could recognize, we should have seen them by now.
Perhaps they do exist, but have progressed so deeply into the unthinkable that we can't even.
Perhaps we will as well.
"The Fermi paradox is the conflict between an expectation of a high {\em ex ante} probability of intelligent life elsewhere in the universe and the apparently lifeless universe we in fact observe. The expectation that the universe should be teeming with intelligent life is linked to models like the Drake equation, which suggest that even if the probability of intelligent life developing at a given site is small, the sheer multitude of possible sites should nonetheless yield a large number of potentially observable civilizations. We show that this conflict arises from the use of Drake-like equations, which implicitly assume certainty regarding highly uncertain parameters. We examine these parameters, incorporating models of chemical and genetic transitions on paths to the origin of life, and show that extant scientific knowledge corresponds to uncertainties that span multiple orders of magnitude. This makes a stark difference. When the model is recast to represent realistic distributions of uncertainty, we find a substantial {\em ex ante} probability of there being no other intelligent life in our observable universe, and thus that there should be little surprise when we fail to detect any signs of it. This result dissolves the Fermi paradox, and in doing so removes any need to invoke speculative mechanisms by which civilizations would inevitably fail to have observable effects upon the universe."
The root of the paradox is that with so many planets in the universe (in the order of 10^24), there must be more life in the universe. But even with this unbelievably large number of potential planets, if creation of intelligent life on a planet requires only 24 independent parameters to be favourable, and each of them are favourable with a probability of 10%, then we should expect intelligent life in just one planet: ours.
Why not? We are definitely the first on this planet, and we don't try to dispute this fact using probability measurements.
An individual (or hive mind, whatever) living in the year 300,000 AD may very much dispute the claim that progress has stagnated. It's entirely possible that civilization has continued an exponential expansion (within limits) from now until then. As such, history is one continued exponential.
Provided that this civilization still is not bumping against the thermodynamic computational limits of space by several orders of magnitude, then the Fermi paradox is still a paradox.
That's how an exponential works, every point sees itself as a privileged point, right before it increases massively.
But I also know I'm missing out on the true space-faring age, the Humanitarian Revolution, the Quantum Age where we begin to fully exploit the laws of QM, the Last World War, extra-solar colonization, etc.
Eventually, if we don't kill or exhaust ourselves with impatience, technology will be solved with respect to providing enough energy and resources for every conceivable human. Then, the real challenge begins. Providing for a population beyond its basic needs becomes an entirely political affair. We may be arrested on the lower levels of Maslow's Hierarchy of Needs for quite some time.
Will humanity observe a similar exponential advancement in humanitarianism as it has with technology? How important is humanitarianism to Fermi's Paradox and the Drake Equation?
Our own survival chances seem to be a fraction not close to unity, but not close to 0 either. Give it 75% to be optimistic. After that, robotic seed space ships could be a buffer to protect from subsequent cataclysms. That does nothing to answer the questions of Fermi's paradox, unless you low-ball to 1.0e-6% chance of survival. Doomsayers guessing such a number are not generally taken seriously.
Looking elsewhere, we have almost unlimited wiggle room in the chance of photosynthesis evolving. Traits that evolved multiple times in Earth's history are inadmissible to this discussion, but several critical traits evolved only once. Fertile but desolate planets are, based on current science, probably abundant. As a typical reasonable human, this is a perfectly sufficient speculative answer.