> The assumption problem can go both ways though, if one can not provide evidence to disprove an extraordinary claim.

So far there is an awful lot of evidence of no extra-terrestrial life on earth: every single microbe shares the same basic cellular building blocks, and often whole chunks of dna/rna. Lots of cameras, radar, satellites and other sensors everywhere that keep not detecting aliens day in day out. We are incredibly certain that space travel is very difficult and will take a very long time (relativity is an extremely well-tested theory, so we're very sure that nothing can travel faster than light). We are actively looking for it and have not seen a single sign of life outside of our atmosphere. So the claim that there is no extra-terrestrial life on Earth has a lot of evidence to support it.

The claim that extra-terrestrial life has visited Earth goes against much of our scientific understanding, it would require a bunch of well-tested theories in physics to be outright wrong. So it is this claim (and not the opposite) which is extraordinary.

> I think such discussion invites at least accepting the possibility of the extraordinary

As far as I know most scientists accept the possibility of alien life, and more often than not are actually hoping that this is the case. But to be convinced that this is the case, rather than it being an unlikely or hypothetical scenario, would take a lot more evidence than a few hundred (currently) unexplained phenomena. For example, some samples of alien tech or biology.

> The presence of UFOs seems to get waved away a lot when discussing the Fermi Paradox. That might be a mistake. Even the US government acknowledges UFOs that they can't actually disprove with scientific analysis.

The US government acknowledges UFOs in the true meaning of the word, "unidentified flying object", they've observed flying objects that they couldn't identify as specific enemy aircraft or drones or whatever. They have also stated that they have no reason to believe these objects are extra-terrestrial in origin. source.

Could these be aliens? Maybe, but lack of other explanations does not mean you can just assume they are, as extraordinary claims require extraordinary evidence.

The probability that someone is the first is 100%, but the probability that we are the first is (presumably) much lower.

It's like you're meeting a whole bunch of people, and you arrive slightly before the agreed upon time, and there's nobody there. Could be that everyone else is just cutting it close, but you'd expect at least some people to arrive early. It's pretty unlikely that you'd be the first one there. So you start to wonder, are you in the right place? Did you get the date wrong? Did you miss an e-mail?