What is the time span for new teeth to grow after milk teeth fell out?

People are different. Baby teeth fall out when the permanent tooth beneath is has started erupt. The permanent tooth has a capsule around it the eats away at the baby tooths root until there's so little root left, the baby tooth will fall out. The permanent tooth should start to come out in a few weeks.
0-8 months. They can be present already when the baby tooth comes out. Sometimes it can take up to 6-8 months. If concerned see a dentist.