It's pretty random I've noticed, sometimes the civilians kick things off really fast, other times they don't do anything. Stuff that helps includes subsidizing the lines, making sure you have reasonably cheap cargo and colony ship designs available(as in, not marked obsolete), and setting up colonies, either on fully habitable worlds or with infrastructure to support civs, you might have to move a few of your own first. It seems that the more population sources you have the better your chances are.
One other thing you could try is SMing in another civ line or two.