I've often thought that Sol would have first approached Barzini first with his deal. Sol would have figured that Vito was already on top, with businesses that were a lot safer than drugs. But Barzini--younger than the other Dons, chafing to be Numero Uno, would have had the most to gain in a deal with Sol. Barzini would have told Sol that he still needed Vito's money and influence. "Go to Tattaglia--he's a pimp, Vito's worried about him. Tell Tatt anything, but I'll be your silent partner." If Vito said yes, Barzini would get silently rich on Vito's money and influence--and Vito wouldn't even know he was making his arch-rival richer and more powerful.
We have to account for Sollozzo's statement to Tom, "The Tattaglia Family stands behind me with all their people."
For Sollozzo, there's no downside at that point to saying that Barzini is with him. Sollozzo wants to look as big as possible. On the other end, Barzini telling Sollozzo, "I'm with you, but let's keep it between us," should have been a sign to Sol that he was being set up to serve as cannon fodder. So that statement only works if Barzini is not on board yet. It makes sense that he joins the group when Cuneo and Stracci do, after the police captain is killed.
