There is no obvious, analogous path to this happening with interstellar travel, even if you stipulate a civilization that has a strong interest and incentive in navigating and exploiting solar system space.
Nearest stars are only a few light years away. The journey might span a few generations. The raft will be a self-sufficient colony that converts onboard matter via fission or fusion to energy, and that energy into every other necessity for sustaining life.
It'll first start out as a proof of concept, only traveling around the local planets. Just like seafaring was first just a fishing thing near the coast. Maybe they try their hand at colonizing Titan first
Then one day, some group will decide to risk it and push off into space. Their distant ancestors will arrive at a suitable planet, and decide to give it a whirl.
All of this is just fun to think about, but just like the settlers of Polynesia 1,000 years ago, it's not unfathomable that 1,000 years into the future, we would have the means to engineer something like this. If we don't annihilate ourselves first.
That's the historical rhyme.
There isn't anything 'only' about it and it's what makes something like the development of ocean navigation structurally completely different. You can swim to an island a mile out and the most isolated island is about 2000 times more distant. Every bit of technology incrementally developed to cover that distance is useful in its own right. Every use of the technology comes with a chance of serendipitous discovery.
Proxima Centauri is 100k+ times more distant than Mars. No asteroid belt miner is going to get blown off course and end up on Sirius. Nobody is going to build the 0.3 ly range ship because it might be good for taking tourists to a mindfulness retreat on Pluto.
It rhymes like pickle rhymes with motorcycle. You have to really believe it.
There are considerable barriers. Just because you can put a number on something doesn't make it practical. To put it another way, what distance between stars would you say would make it impractical to spread between them via colonisation? Where would you put the threshold?