And even earlier than that they just used colony ships travelling at or under light speed.
I'd forgotten about the Ohnyl Colonies from Flight of the Eisenstein, which look to be mirrorless O'Neill Cylinders and were -- according to Lexicanum without citation -- apparently used for the habitable section of plasma-driven generation ships.
If that's true, it suggests that the Age of Terra, at least, may not have been as stable a golden age as has classically been assumed. Interstellar travel is always a balance between trip time and fuel cost; the slower you go, the less engine you need, but the longer the ship has to work in the middle of literal nowhere without breaking. One of the most commonly hypothesized ways to cheat this is to offload the reaction mass for either or both ends of the trip onto external sources; if you put a magnetic sail on your colony ship, you can let Earth direct a mass beam toward it for the boost phase and flip it on again to decelerate against stellar wind on the deceleration phase, and the whole trip doesn't need much more than reaction control fuel modulo any concerns about drag losses in cruise phase.
Now, there are plenty of reasons not to do that and instead haul all of the deceleration delta-v up to cruising speed with onboard engines, but there is one dramatically useful one that is resistant to engineering solutions: If Earth decides to shut off the mass beam partway through the boost phase, the ship is effectively stranded.
It's admittedly not certain, but I kind of like the thought that perhaps one of the drivers behind pre-Imperial human space's diversity is that the people doing the colonizing couldn't rely on the cooperation of the people on Earth.