I think it starts off a bit earlier, when Vito calls the grand meeting to end the Tattaglia war and allow Michael to come home from Sicily (right after Sonny gets killed).

Tom Hagen: When I meet with Tattaglia's men, should I insist all their drug middlemen have clean records?
Don Corleone: Mention it, don't insist. But Barzini will know that without being told.
Tom Hagen: You mean Tattaglia...
Don Corleone: Tattaglia is a pimp. He never could have outfought Santino. But I didn't know until this day that it was Barzini all along.

It was at that meeting that Vito realized Barzini engineered the hit on Sonny by getting Carlo Rizzi to lure out Sonny into the open. That's why he warned Michael about the Barzini deal -- he'd have to flip another Corleone member to kill Michael.