This is extremely unofficial and strictly IMTU so take it with a grain of salt.
Regarding initial colonization, I assume there is a target world that is about to be settled. I roll Starting Population with 1D-3 with a minimum of 1. I then roll the Pop Multiplier with a straight 1D.
I apply DMs based on the target world. Clearly Ga attracts more interest than De, for example.
This generally gives a start-up colony an initial population from 10 hardy souls up to 6,000 bright-eyed colonists.
For the migration phase, I use 50 year turns, each turn rolling 1D which is added to the Pop Multiplier. Again, DMs based on the physical trade codes of the world. When the Pop Multiplier hits 10 or more, the Pop digit ticks up one and the remainder becomes the new Multiplier.
So the big 6,000 person colony (Pop 3^6) rolls a 6 for growth, that gets the permanent Pop to 4^2 or 20,000 people after 50 years. I re-roll Government and Law Level at this point, and take a look at the starport and TL as well. If it had instead rolled a 2 and only grew to (Pop 3^8) 8,000 people after 50 years, well, I guess there's something happening there - very little interest to new colonists, tougher conditions than expected, political shenanigans, mega-corp issues...
The Pop increase works great for "core" or well-settled areas too when advancing the overall timeline of a campaign.
As I said, decidedly non-canon. But hopefully it will give you some ideas if nothing else.