My hypothesis is that, if given a (simulated) spectroscopical observation of Earth's atmosphere from a distance, astrophysicists would come up with plausible non-biological, non-industrial explanations for it.
Empirically, we've just had our first occurrence of astronomers not being able to explain a compound in a planet's atmosphere, and it's something much easier to deal with than a massive amount of oxygen.
I think they would settle on the opinion that any explanation would be about as interesting as life. But not fully settle on life.
Would fluorocarbons be detectable in a remote spectrogram of the atmosphere at the levels they existed in the earth's atmosphere? Would the depletion of ozone in the atmosphere be more visible?
From [0] it looks like CFC's peaked on the order of 1 ppb. Humans (perhaps) just detected phosphine at the level of ~20ppb in Venus's atmosphere through telescope spectral analysis [1], but that's on a very close planet that we've been staring at intently for 4000 years; presumably there are compounds present in smaller concentrations that we haven't seen yet. Is there a heuristic for the hypothetical minimum sensitivity relative to interstellar distances?
I think they would settle on the opinion that any explanation would be about as interesting as life. But not fully settle on life.