This something I posted elsewhere as a response to a comment on a discussion about aliens which mentioned that the distances between stars in the galaxy is very large and difficult to cross.
The real problem is that the distances within a galaxy are too short.
We pretty much know how to travel between stars at 1-10% of the speed of light. There’s probably a few centuries of detailed engineering work to get from here to there, but the physics works and doesn’t require impossible amounts of energy. At the high end of the scale we can colonise the entire galaxy in a million years, at the low end in ten million.
So if expansionist technological societies typically evolve more than ten million years apart, the first one will take over the galaxy before the second has a chance to evolve.
Someone has to be first, and right now it looks like that’s us; if someone else was out there and even a few tens of thousand years ahead of us we should be able to see evidence of their existence from here. I could quite imagine that they have evolved and then wiped themselves out or gone introverted rather than spread across the galaxy, but that makes them just a footnote in galactic history.
We can see oddities in other galaxies which could be signs of engineering on a massive scale. But intergalactic travel at even 10% of the speed of light would take a very long time.