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I don't think this gives appropriate weight to exponential growth.

If humans are ever able to leave the earth and even theoretically establish permanent habitation, it's unthinkable that no other civilization has done so.

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Even so the galaxy (let alone the universe) is huge, and faster-than -light or extra-dimensional travel is probably impossible. Contact with another civilization is extremely unlikely even if life is abundant in the galaxy.

Check out von neumann automatons. The idea is that once you started colonizing, you'd cover the entire galaxy in ~a million years, aka very quickly on a galactic timescale.

https://en.m.wikipedia.org/wiki/Self-replicating_spacecraft

A galaxy is very tiny on the scale of the universe.

Sure, but the gp said galaxy.

the universe is huge and time is long, there could be millions of civilizations and we could happen to exist at a time that doesn’t coincide with a single one

The universe is extremely young. We might just be tied for first, if it takes 3rd generation stars for example.

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