That’s roughly the premise of several sci-fi short stories and novels I read (and of which I can’t name at least one after having read several hundreds of those).
It’s sort of done in The Three-Body Problem.
Doesn’t matter. Any intelligent alien species smart enough to interpret radio frequencies could also see the Oxygen and Methane in the atmosphere and figure out there’s life.
Additionally, they’d see all the CFCs, and manufactured chemicals we’ve been dumping into the atmosphere and know there was post-industrial life. The way our sun’s light interacts with our atmosphere makes a bigger signpost than any radio broadcast we can make.
We’ve been announcing our existence to the universe ever since the Great Oxygenation Event, if not before. All they need is a telescope and basic spectroscopy from the chemical signatures of our atmosphere.
https://en.wikipedia.org/wiki/Great_Oxidation_Event
There’s a bird in the forest, plain for all to see, if they look. But they’re not looking until he starts singing.
(Serious, does that analogy stand up?)
Depends on the alien species: We humans are already looking at other planets and their atmospheres, and we have no hope of going there or making contact with anything even if it exists.
If they are anywhere near as curious and as advanced as humans, they’ve probably spotted us already. (well, “as advanced as humans”, we’ve only been able to look at other planet atmospheres since like ~2016, when ever certain satelites launched, soo…)
“Two possibilities exist: either we are alone in the Universe or we are not. Both are equally terrifying.”
― Arthur C. Clarke
