Consider the following timeline.
Assume Islam emerges in 300 AD rather then 600 AD; if so, would it have survived and developed?
My answer in emphatically NO!!! But why?
Because Rome ruled the world in 300 AD and would never have tolerated Muslim belligerence and insolence.
In contrast, Roman Catholicism survived and thrived because it was never perceived as a threat to the authority and order of Rome.