Interstellar probes will get to be pretty cheap with sufficient economic growth. We should be able to easily afford >0.1c probes in 100 years or so on our current economic trajectory. And if our civilization advances for another 1000 years they'll be a piece of cake.

If those probes are Von Neumann machines they can spread throughout the entire galaxy in as little as a few million years. That's the crux of the Fermi Paradox - on galactic timescales any sufficiently advanced civilization should be able to expand its presence to the entire galaxy pretty easily and quickly.