We're already sending out a signal into the cosmos (and one more powerful than the radar signals others have mentioned)- the recent sharp upswing in CO2 over the last hundred or so years [0] would look markedly artificial, which combined with the presence of oxygen (which wouldn't stay in the atmosphere if it weren't continually renewed) strongly indicates at least a complex ecosystem, if not directly implicating an industrial civilization. Detecting light reflected from exoplanets is something we can already do, or nearly so, so we can count on this being detectable from large distances by alien civilizations with access to potentially megastructure-scale space telescopes. At that point, any reasonably curious or concerned ETs could send a probe to get a closer look.

Earth, as far as we know, is an unusual planet, and obviously so. Either we're wrong, and there's Earths all over the place, or we're alone, or ET has been keeping an eye on us for a long time already; that we're "hidden" is hard to imagine.

[0] https://www.co2.earth/co2-ice-core-data