It is possible to pick up extremely weak signals, even if there's background noise. For example, and this is radio and not sound but it illustrates an interesting point, the Voyager space probes are in interstellar space and their transmitters aren't any stronger now than they were when they launched. However, we're still able to communicate with them.

Point a very sensitive antenna at the sky right near, but not at, where you're looking for the signal; what this antenna will pick up is the background noise. Point another antenna exactly at the Voyager probe; this antenna picks up the background noise and the probe's signal. Subtract the two signals from each other and you're left with just the probe's signal.