Otherwise you are just a Hobo jumping on a passing train and hoping it ends up somewhere hospitable so that your great great great great great ... great... great... great... great grandchild, an lineage born and lived entirely on the train, has a place to call home.
Without FTL, to spread over the galaxy we'll need to adjust our thinking on long time-scales for any of it to make sense or be possible anyway. We'll be a different species really (or _several_ different species).
If I were to bet, I'd say our more lasting contribution to the galaxy will more likely be mechanical (AI) descendants rather than ourselves, and next most likely would be barely recognizable biological dscendants (not necessarily that different from us physically, but in terms of society and mentality). That's all assuming we make it off of Earth and then away from Sol at all in any lasting way.
If you can live for 10,000 or 100,000 years then being limited to lightspeed isn't such a bummer. You can visit interesting places.
https://www.fourmilab.ch/cship/flythru.html
You'd have hundreds of years of media to catch up on when you got back.
If the AI doesn't absorb us somehow, I suspect it'll limit our ability to contaminate the rest of the galaxy.
(In the infosphere the Earth shines alone in darkness, the sole star.)
The machine will keep us in a bottle to feed off of our data.
...
Come to think of it, why wouldn't it "farm" us over a larger volume?
If an AI comes from space, it's likely billions of years old and we are as interesting as fungus.
> I don't see how humanity is a source for information beyond the initial growth phase (assuming it's created here on Earth).
Setting aside the possibility that Earth life is already an ancient alien nanotech AI ( https://en.wikipedia.org/wiki/Panspermia ), and assuming that humans are unique in the Universe, the rest of the entire Universe is pretty much predictable. There may be some poetic physics going on out there (I mean, of course there is, the Universe is beautiful!) but unless there's another planet of insane ape-men out there somewhere ours is the only show in town.
I imagine that the limitations of organic lifespan limitations will disappear with our species.
The most we can hope for is that AI somehow takes us with it.
Everything we do is survivorship bias. On Earth we may be the gardeners, but in space we're just the seeds.