If I Pull Out a Hair, When Does It Start to Grow Back?

If a hair is pulled out prematurely but the hair follicle isn’t damaged (brushing, drying your hair too roughly with a towel), does the next hair begin growing ‘immediately’, or does it wait until the next hair cycle (which could be many months away)?

Also if a hair is pulled out prematurely is there a risk that the hole in the skin could heal / close up before the next hair has a chance to grow out, especially if the hair is miniaturized?

If you pull out a miniaturized hair, it might be permanent (depends upon where it is in its loss cycle). Generally, pulled hair (healthy hair that is) will return fairly quickly after it is pulled out and the pore that it exits from does not close up.