ENT "Terra Nova" is pretty informative here: it establishes that
a) the colonization described there was the very first attempt at Earth setting up an interstellar colony, as far as the history books of 2151 can tell
b) previous efforts included successes with New Berlin at the Moon, Utopia Planitia at Mars, and a few asteroid colonies
c) colonization was by the warp-capable Conestoga after a nine-year flight that launched in 2069 and arrived at a location less than 20 ly from Earth in 2078, dubbed Terra Nova
d) the colony soon cut contact with Earth but survived till 2151
What the episode leaves open is whether other colonies were founded earlier on without the knowledge of Earth, but no other episode has revealed the existence (brief or ongoing) of such colonies. Given the timing, such a founding would probably have been without the benefit of warp drive, or then relying on a warp ride provided by aliens.
We never explicitly hear of a human colony launching a second-generation colony. Yet we do know that the colony at Deneva can build ships for further colonization as of "Operation: Annihilate!", so second-generation colonization must be at least theoretically possible.
We learn that as of the ENT era, human settlements exist at Proxima (possibly the real Proxima Centauri) and at Vega at least, the former actually closer than 20 ly to Earth if the assumption is correct; supposedly, this location was still deemed unsuited for colonization back in 2069. Tellingly, so was Mars, according to VOY "The 37s" - perhaps the early Utopia Planitia colony failed?
Since a great many DY series ships are listed as founding interstellar colonies in the 22nd century, it would stand to reason that vessels in the series were at it in the 21st century already, as "Space Seed" does not appear to make any significant distinction between the interstellar propulsion capabilities of DY-100 and DY-500. Supposedly, neither type had warp drive, but refitting is always a possibility.
Timo Saloniemi