That's a good question, MC! The movie leaves it open, suggesting (at least to me) that Vito's death was the decisive factor.
But the novel is clearer: Even before Vito dies, he and Michael have a chat in which he says that he's going to make his moves after Kay has the baby and to give Hagen time to be settled in Vegas. He estimates that it'll be a year from the time of that conversation. Vito appears to have doubts: " 'You've prepared for everything?' He did not look at Michael when he said this." Michael seems to sense the Don's diffidence: "You have no part. You're not responsible...I would refuse to even let you veto. If you tried to do that I would leave the Family and go my own way."