A 'generation ship' could be just a bio-lab and genetic material (possibly digitized) that is grown into life only after the destination is reached. Or after it is terraformed by other genetically altered organisms, engineered on-site by AI (or by Earth-based scientists, at the cost of a few communication round-trips).
And this is just the most basic version someone from the 21st century would come up with.
Edit as reply because I am "posting too fast": From TFA: We are not gods
A cheap way of dismissing what is already, today, nearly working technology - artificial wombs [1], and building genomes from scratch [2]. Further, what I proposed is basically equivalent to seeds - as in literal, existing plant seeds. But we won't be able to replicate, in 10000 years of technological progress, what nature already has working? Such a claim requires showing some strong, fundamental barrier, not to have the possibility handwaved away with "we are not gods".
What technological progress can't be dismissed with "we are not gods"? Landing on the moon? Splitting the atom? Heart transplants? Heavier-than-air flight? Fire?
[1] https://en.wikipedia.org/wiki/Artificial_womb
[2] https://www.theguardian.com/science/2010/may/20/craig-venter...
OK. Give me the keys to your time machine, so I can take a look at what "technology from 2000 years in the future" will look like.
You appear to be confusing fantasy for reality.
From TFA:
We are not gods, and anyone who thinks of science as a magic wand, or even as a verb, is making a mistake, a category error sometimes called scientism. Drill down a little harder on these issues, look at the evidence; use the scientific method properly. Limits to what we can do will quickly appear around you.
When's the last time someone making this argument turned out to be right in the long run?
The fundamental physical resources needed to launch and land enough material for an independent colony, even on our moon, would strip Earth of the things needed to sustain us here.
There may be more fruit out there, but it's on other continents while we live on an island atol with a single tree.