Everyone has made similar points here, and I agree it was more a process than anything else. I think it begins after Vito is shot and Michael is observing up close how badly Santino is handling things. It dawns on him that if the family is to survive he is going to have to become more invlved. So he goes into NY and blows off Kay, goes to the hosital and his worst fears about how this is being handled are confirmed. The guards have all been sent home, and Vito is about to be killed. This is folllowed by the "I'm with you now Pop," scene, followed by Michael cleverly using Enzo to bluff the assassins, followed by him openly accusing McCluskey of being on the take. The following day when he returns home
everyone he learns the war has been escalated by Sonny who whacked Tatt jr (in exchange for a slap in the face???) and he sees everyone in the family hemming and hawing about what to do next, with Tom leading the charge to neotiate a deal. Finally he realizes he is the one ho has to stop Sol, and then when he does it he crosses the Rubicon, so to speak. Then after Appollinia's death, he knows that he is the only surviving son who can save the family. When he is in vegas his attitude toward Fredo is cold and distant, and by then he is a fully developed bad ass.