Ruler: "Advisor, when do you think the province will grow to the next rank?"
Advisor: "We are very close milord. We only need 23 more civilians and a few dwellings, and we have enough populace to level up. If you manage to keep a major war out of the lands, I imagine the province will be level 4 in no more than a week, perhaps two."
Ruler: "Screw that, I need the income. I'm kidnapping 23 peasants from our neighbour. Gods willing, we'll be lvl 4 tomorrow!"
...
Personally I kinda like the "slow" way of things. Always struck me as odd that a province suddenly had an influx of citizens, just because some lord used a bit of "influence" and had a lucky die roll.