Since travelling faster than light will probably never be possible, people assume that humanity can never defeat the distance to a habitable planet in a another solar system.
But if it is looked at strictly as a matter of travel time, then the technology for moving to another terran planet is almost within our reach already.
Yes, we have to accept that those who left our system will never arrive at the destination — but their descendants many generations down will.
FTL travel is possible, we just don’t know how it’s done.
Multigenerational colony ships would have to be preceded by some sort of prospector missions, high-speed sprints to the nearest stars, to survey any systems they find and send back the data (which would just take a few years to return; the mission would take more than a human lifetime).
Once a candidate planet or two get identified, a big seeding mission (plants, beneficial microbes, perhaps some forms of multicellular animals) would have to be assembled in orbit, then sent at a velocity appropriate for eventual looping braking at the candidate star and planet.
The colony ships would likewise be built in orbit, stocked with every kind of information needed, some kind of self-sustaining food supply (including the food crops which the planetary colonists will rely on), communications, and probably technology to make fuel in different ways for those “just in case” unexpected scenarios. They could start some years after the seeding missions. And they’d have to include something that could make the landings possible and still be in working order after literally centuries en route.
I’m not optimistic a multigenerational colonizing mission is feasible. And as in sci-fi, by the time the colony ships reach the destination, they’ll likely find themselves overtaken by events, arriving at a world that has already been colonized by people arriving aboard FTL developed after their ancestors set out.
:’)