Space is big. Really big. It’s such a long way to the nearest star to Sol that I expect a billion people living in a floating Pacific seastead community before I the first hundred thousand reach the stars.

Unfortunately, once we do have proper cheap space access with e.g. a launch loop, the exponential nature of growth means it only takes 50 generations of 4-child families to go up each step along the Kardeshev scale.

After type II, population growth is limited by the speed of light.