Basically, the universe is so ludicrously huge and so ludicrously old that it is as close to statistically impossible as one can imagine that human beings are the only things ever to evolve in such circumstances as to be sapient.
Note that the paper you have linked uses the term "detectable civilization", which is significant limitation due to our current level of technology, the age of the universe, and the propagation speed of light. It wasn't that long ago that we couldn't even detect extra-solar planets.
There is of course an argument to be made for us being "alone" in the universe in the sense that sapience is rare enough that pretty much all species, including ourselves, will die out before ever meeting another sapience, but the idea that in all the unimaginable vastness of the universe we are the only ones?
Maybe even out of 1,000,000,000 of similar universes only 1 would actually happen to have life. It's similar with planets. If you only know of 1 planet within 1B to have life, how can you tell the odds are not low enough to have 1 universe out of 1B to have life?
This could be an awesome example of survivorship bias to assume because there's life here, there must be life elsewhere in the universe too. We only have experience with a planet where there's life, so we are innately biased to think that it might be more frequent occurrence than it really is.
In other words, the fact that it has happened at least once very strongly suggests it has happened more than once.
No, it doesn't at all.
Maybe just the opposite.
The universe is mind-bogglingly large, but it's also really, really empty, and really, rally sparse. The numbers games starts to dwindle very quickly in terms of all the ingredients necessary.
And the Fermi paradox helps provide crudely indirect evidence.
If there was any validity at all to the 'common life theory' - then it would have started long ago and probably spread everywhere to the point wherein there would probably be ample evidence.
In the 'common life' scenario, it should be rare/impossible to find life that's disconnected from other life scenarios.
There's a decent chance we are alone.
The common argument in favor of more life is that the probability of life evolving is some very small number, such that there must be a very large number of opportunities for life to evolve in order for life to actually evolve. At the same time, there are a large number of opportunites given the size of the universe. Given that there is presumably no relation between the "small" probability for life to evolve and the "large" number of opportunities in the universe, we don't expect these two numbers to conspire to be near the same size, which is what would have to happen for just one life to evolve. Rather, we expect there should be lots of life that evolved in different places or that the probability that any life evolved at all is extremely (vanishingly) small. So if this argument is correct and we know of one life form, we should expect many more in the universe. (Not to imply we would necessarily be able to find them.)
There is one potential problem with this argument. It assumes there is just one universe. If there are many universes then it is possible that life did not evolve in almost all of them. In universes where life did evolve, odds are it happened just once. And of course, that life (us, for example) would see that univese and the life that evolved there, however improbably that would be.
I read a saying "You know an argument is wrong if it invokes quantum mechanics." But I'll do it anyway. Some educated people believe quantum mechanics works this way - the univese effectively branches into parts that are essentially distinct (referred to as different universes too). It is not as outlandish as it may seem. The whole reason quantum computers are supposed to be powerful is that different things happen in parallel.
You don't have to buy the quantum mechanics part. If there are multiple universe for whatever reason then the probability argument above is not valid.
I do want to add one thing. The number of "opportunities" for life in our universe grows linearly with each dimension in the universe. (Lets just say to the fourth power of the size of the universe.) On the other hand, the size of probability grows/shrinks exponentially. So it is not hard to imagine between the two of these numbers, the exponential one wins.
The non-existence proof of ETI also means laws of physics are cruel and cannot be violated. There is almost 100% chance that advanced life forms exist in other galaxies, may be even billion year old. But no one has figured out how to travel faster than light.
If anything I'd hazard our ignorance is more on the side of things we don't know we haven't observed than things we observed incorrectly.
I think compared to how long it took for somewhat intelligent life to evolve on Earth, from the point of first life. Assuming* a comparable evolutionary cadence, the question then becomes - how often does life begin?
*This I assume because the cadence of living things on Earth is at the very least tied to the day/night cycles, winter/summer seasons, and lunar tides, none of which are especially unique.
the most convincing meta-analysis i've seen, which considers the probability distributions implied by the error bars in our current best estimates of the relevant parameters (https://arxiv.org/pdf/1806.02404.pdf), suggests a 39–85% chance we are alone in the observable universe. i'm less impressed by those particular numbers than by the attempt to rigorously quantify our ignorance on the issue, where some component values span fifty orders of magnitude. while the universe may indeed be big, i'm not sure it's broader than the sheer span of our ignorance.