This is a bit off on a tangent, but for anyone interested in this subject I highly recommend reading Stephen Webb's book "Where is Everybody?", in which he goes over and lightly refutes 75 possible answers to the Fermi paradox in three main categories: 1) aliens have already been to Earth (and may still be here), 2) aliens exist but we haven't had any way to interact with them yet (and maybe never will), and 3) aliens don't exist.
He covers most of the popular theories - the zoo hypothesis, the great filter, aliens hiding from us, inter-planet communication being unsolvably hard, life being extremely rare, our planet having uncommon characteristics, alien life being fundamentally different to life on Earth in a way we can't comprehend, etc. and the common rebuttals - we haven't seen or heard signs of intergalactic civilizations (which we believe we know how to detect at this point), von Neumann probes haven't come to dismantle us, different alien societies would likely have different goals and outcomes (which invalidates the many theories that are worded like "civilization will always eventually ____"), etc. It's pretty thorough and a very fun read if you're into that stuff.
Notably, though, one theory he doesn't address in too much detail is the idea that evidence exists but is rare enough that it can be covered up effectively and not all governments have it (so there doesn't need to be global cooperation). Throughout the book his stance is basically "it's a hard fact that we have no evidence of aliens", which is obviously at odds with conspiracy theories about coverups. Despite not generally being a conspiracy theory guy, I personally lean in this direction because after reading his book, the other solutions in which aliens do exist don't seem particularly appealing and I do hope that aliens are real. He also shares his own preferred alien-less solution at the end, which I found to be a bit somber but very reasonable.
As for the question in this thread, I'd be convinced if any one major government (US, China, Russia, Germany, France, etc.) officially acknowledges it. It could be that they decide to come out and share the evidence they have. Or, perhaps more likely, it could be that something happens that's substantial and compelling enough to convince a huge amount of people that aliens are real, and the government is forced to respond with a confirmation, which I would treat as the moment of certainty.
https://www.goodreads.com/book/show/180506.If_the_Universe_I...