Actually, Enterprise has established that Alpha Centauri was the first out-system human colony. It's only mentioned once however, and in passing, at that, so its easy to miss.
I simply adapt the Centauran background, to say they were colonized via sleeper and generational ships and when they arrived, they established a utopian society which became the Centaurans of the RPG universe.
It requires a bit of revising of both canon (ie Enterprise) and the RPG, but it allows everything to mesh with a minimum of fuss.
Vash: They weren't exactly thrilled to see you on Brax. What was it they called you? "God of Lies?"
Q: They meant it affectionately.
Q-Less, Star Trek: Deep Space Nine