But that's not actually true. We've been "broadcasting" the fact that there's life on Earth in the form of the spectrographic signature of an oxygen-rich atmosphere, which is a clear sign that photosynthesis is going on. There's no geological process that could maintain that much oxygen in the atmosphere. The Great Oxidation Event is when that started.
We have the technology to detect this kind of thing already, at our current level. Any civilization that could reach out and attack another solar system would be able to very easily see it.