Fermi Paradox

Hi.

I was wondering: How do we know it would even be possible to receive
the signals from aliens even if they did exist and did send out radio?
Considering we have a galaxy full of stars blasting out far more
intense radio signals than any ground-based transmitter could.
Wouldn't it be like trying to listen for a fly buzzing on the other
end of a stadium, with 50,000 screaming fans in between you and it?