A solution to the whole Population problem are increasing the food policy (1,25 food instead of 1 food per pop) and using the food policy. If you get a good farming world, its rather easy. Also, Robots, fill as many worker jobs with Robots as possible (very good way to quickly expand colonies). If you get Androids, use Androids too, build as many as possible. If you have improved robots on your raw material worlds, you should be able focus your normal pops on Industry, Culture and Military. Also, City planets have crazy Population growth, since they not only get their own growth bonus, but usually also have massive immigration.
Also, another, slightly cheesy novelty tactic. Set your refugee policy to "Our Species only", make a Migration pact with a smaller empire you're not interested in and wait. If that empire gets hammered in a war or f.e. a Khan, refugee pops of your own species will start fleeing to your worlds. (I'm a bad person)