My GUESS would be that if your goal is conquest via demographics, then starting early would be part of the plan. Genghis Khan had in interesting theory about muslims, i.e. that if he killed enough of them, Mongols wouldn’t have to outbreed them...
Genghis Khan was a very wise man and had the right idea.
deporting a moslem only perpetuates the problem. They need to be eradicated.