The problem with world conquest is it gets awful tedious after a while.
The problem with doing it as a muslim is decadence gets out of control after a certain size. After about 1000 holdings -- maybe 1/3 of the map or so -- a single son can generate absurd decadence. As long as you keep up the holy wars and invasion, you can keep knocking it back down but it's really not fun. You feel like there's this constant death clock you can't control ticking against you. If you're going to start as muslim, at some point you're going to want to find some way to become Christian -- which isn't an easy switch to make the game do.
Your best strategy is probably to start in the middle of the map with a Christian power with the Aztec invasion enabled. Use a lot of papal invasions to expand into as many Christian kingdoms as you can. Once the Mongols and Aztecs arrive, everything to your east, west, and south you should be able to holy war. As soon as you can do it, take the Roman title. Become Orthodox and form Rome. You can then use the Roman conquest CB to mop up most of the rest of Christian Europe where you can't holy war. Also mending the schism will let you holy war Catholics. If you need to, embrace an Orthodox heresy and you can holy war everyone.