"First to leave our rock" is specifically what I'm suggesting as a possibility, not first life or first intelligent life.
How could we ever know that though? The chances that we'll ever be able to contact, let alone even see except as as a tiny bit of light that looks like another star, another galaxy is virtually zero. And we're one of at least 125 billion. It's a nice thought, but I just can't think that we are somehow so special as to be the first in the entire universe. I mean yeah, we could be. But damn, the universe is 13.7 billion years old (well we know it's at least that long because of light, I think it's also kind of arrogant to state that the big bang is a fact), and humans have been around for a couple hundred thousand... our planet has been around for 4.5 billion years. Sure, it would take a certain amount of time for it to be possible for this level of complexity of matter to crystallize from the early universe, but imagine an earth-like planet somewhere in the universe (there have to be many, just statistically), that formed at the same time as Earth (again, a great many of these across the 125 billion galaxies)... imagine that instead of 5 mass extinction events, this planet had 4. Its equivalent of humans could have gotten to this point millions of years earlier (or even tens of millions).
or 2. the distance between two co-existing intelligent lifeforms is virtually insurmountable while the speed of light remains a physical ceiling. Or maybe both, or itโs vastly more complex than that.
Either way, evidence of alien life = nil. I donโt believe in something until thereโs evidence. Sure, itโs fun to think about and write science fiction about the topic, but itโs just that โ fiction.
The second item you listed is most likely exactly the truth. But your conclusion is just not something I can really jive with. I mean yeah, okay, we can't know either way, so you just have to go with logic as to which probability is higher. If we know and acknowledge that the universe is incomprehensibly vast - it takes light 100,000 years to travel across just our galaxy... the distance between galaxies is even greater, and there are over 125 billion of those... well I described it before. It just seems (to use a great word from someone else a bit earlier) solipsistic to think that it's more than a vanishingly small chance that our star is the only, one of out (using our galaxy as a template, though ours is bigger than many, but smaller than many, too) the number that is 1 billion times 125 billion (that's 20 zeroes)
at least, that was able to develop life around it. I agree that it's likely a moot point for our everyday lives, it's probably something we'll never know, but we can still arrive at the conclusion that it's very much more likely that there is other life in the universe, vs us being the ONLY life in the entirety of the cosmos. The latter position has a similar sort of ring to me as "we are the chosen people of god". We are really not that special. Or maybe we are quite special, but even if 0.000000001% of planets with liquid water (and we have a moon of Jupiter in our solar system that is literally full of liquid water except for its core... either our solar system is chosen by god, or water isn't that uncommon) form life, that would still make for a number in the known universe of an order of magnitude of 12 zeroes - a trillion.