I also agree that Barzini was in it from the beginning but I come at it from a different direction than Wayne's:

Sol needed three things: to operate under the umbrella of an established NY family, working capital, and police and political protection. But he also had something to give: the money his partner made with him would make the partner stronger--perhaps strongest because of the profitability of drugs.

Any family could have given him the umbrella and maybe the working capital. But only Corleone could provide the police/political protection. And Corleone didn't need his profits because he was already Number One with businesses that were far less risky than drugs.

So, I believe, Sol went first to Barzini, who he recognized as younger and more ambitious than the other Dons, impatient to be Number One, and more needful of drugs profits. Barzini would have said, "Your logic is sound. But you still need Corleone's police/political protection. If you tell him I'm your partner, he'll say no. Go to Tattaglia--he's a pimp. Corleone isn't afraid of him. Tell Tatt and Vito anything you want. But I'll be your silent partner. And I'll have your back."

Barzini couldn't lose. If Vito said yes, Vito's capital and police/political protection would help make Barzini (through his partnership with Sol) stronger. If Vito said no, Sol would try to kill him. If he succeeded, Barzini would be Number One by default. If he failed, Vito and Sonny would come after Tatt.