When did first become bandits?
Mohmad stomping toward Mecca from Medina with a force of around 10,000 had quite a lot to do with Abu Sufyan giving up Mecca without a fight. And, after he surrendered the city, he, of course, converted... as did everyone else in the city... or else, as per usual with Islam even to this day.
The Qurash were the tribe of Mecca and a compliant Qurashi was put in charge of them as a new part of the growing Muslim Empire.