By that token, the paradox makes some sweeping assumptions about the efficacy of interstellar communication to begin with. Space is big, and interstellar communication almost impossible unless both parties already know and are already expecting communication. Establishing first contact across interstellar distances is like trying to shoot a bullet out of the air with another bullet fired from two different guns in two different states; you'd need an exceptionally powerful gun with even more exceptional precision. And the other guy has no idea you're aiming at him. But you, the shooter, are doing on purpose; two bullets don't collide by chance. First Contact happens when one civilization already knows about the other one before hand and so they send a deliberately overpowered signal to reach out.

It's possible, to be clear, and hell it may have already happened. We just haven't been listening long enough to know.

I don't think breathable air counts as signs of industry. Although looks like JWST has found a planet with carbon dioxide which is interesting.

So you are right I guess that it could possibly detect industrial emissions.

Interestingly enough the planet with CO2 found is 700 light years away which could hint at industrial life there (but still going to be pretty hard to be certain), but if they were looking at us then they would only see Earth's atmosphere 700 years ago which would have a lot less CO2 then now.

But anyway in terms of electrical emissions, radio waves or seeing constructions on surface (or even orbital) I think it's pretty hard to get anything from the nearest solar system to ours, you can't just take a quick photo so everything is going to be super blurry

To give some more thoughts on the matter, much is often said about the probability of life in the universe, and the possibility of life's emergence in any given scenario. Leaving aside for a moment that developing probabilities with a sampling size of 1 is ludicrous at best, the method behind the conclusions--reverse engineering the requirements for life to evolve at least as we understand it to get some idea of what might likely be out there--can be flipped in the other direction.

We know, from our experiences, at least a little of what it takes to develop life. As far as we can tell, life on earth emerged from a single ancestor, which is to say we have one tree of life on earth that traces its roots back to a common ancestral microbial organism from which all life emerged, and all life shares family with. This original life form is an "emergence event" for life. Should life exist on Mars or Europa or even early Venus (which likely was a water world), it too would have had one emergence event similar to ours, and that life will have evolved along its own branching paths in its own tree of life. What then does it take to develop intelligence out of a microbial organism?

Because the discussion around the search for aliens usually implies the search for other intelligences, ones capable of using technology to communicate over vast distances, develop civilization, and explore the cosmos. Microbial remnants on Mars, aquatic animals on Europa, or whatever might have existed on Venus 500million years ago wouldn't be the holy grail first contact scenario we like to envision, though such discovery would completely change our understanding of life in the cosmos more generally; in one solar system, life will have had up to potentially four distinct emergence events, maybe more. The next question one might ask is, what happens if life emerged more than once on a single planet?

But our concern is with intelligence. Intelligence on earth had its own, distinct emergence event about 200,000 years ago with the emergence of homo sapiens. The thing is though, depending on how you define "intelligence", Earth may have had more than that. If you define intelligence as the capacity to make and utilize tools fashioned from the environment to better improve the odds of survival, than numerous species across the Earth already engage in that, from small maki monkeys using basic hammering implements, to Otters building dams, to other primates using weapons. Even homo erectus and other sub phenotypes of humans, distinct from Sapiens, used tools and built small communities; they now remain silent, but they existed nonetheless.

If you define intelligence as the capacity for language and communication along complex social structures or the ability solve complex problems, again, we see that all over the world, most notably in dolphins, who use a truly complex communication style to form sophisticated battle strategies in either hunting or playing, form social structures, and seem to hold very human like feelings for others--good or ill. And of course, primates have been able to learn sign language to communicate with humans. They even have senses of humor, and it's been argued they even have names.

If you define intelligence as self awareness--or sentience, the ability to recognize ones own feelings either physical or emotional as oneself--we see that everywhere. Dogs, parrots, primates, dolphins, elephants, and many more can look in a mirror and acknowledge that they are themselves, the foundation of consciousness, what one might call the soul.

And if you define intelligence as the capacity to develop civilization, and claim that humans are distinct in that category of all life on earth, than I would argue that civilization is merely the cooperative expression of beings that build with tools, communicate with language, and recognize oneself in the mirror as distinct from others in the group. In my view of the Earth, intelligence has had not one emergence event on Earth, but in fact dozens of emergence events, with humans being the obviously most advanced--but nonetheless only the greatest among many.

And at the risk of sounding conspiratorial, I can't even say with certainty that we were the first. We have no direct evidence of intelligence before us, but we also can't discount the possibility; intelligence's frequent reemergence in our tiny window of time would suggest that complex life naturally lends itself to complex, problem solving brains that lend further to the emergence of intelligence. What, then, may have existed 66million years ago, just before the fall of the dinosaurs, when the oxygen was richer and the life on it larger? What may have looked up at the stars and wondered to themselves--in their capacity to understand that they are themselves--what else might be out there, and what else might yet come?

In this view, while we can't say for certain how common life is, we can say with some degree of certainty that, where life does emerge, intelligence is not that far behind.