Why Haven't We Seen Aliens?

The furthest we've sent a probe right now is just barely outside this solar system. That's like, bazillions of miles away. But if you were thinking about it on long time scales, it's not going to take like millions of years. So that's a really interesting argument because it suggests that with technology not super far in our future, some other civilization could have explored the whole galaxy with self replicating probes. Are there no other advanced civilizations out there who have this idea?