It is pretty much conventional wisdom that Barzini's long term goal was to move the Corleones out as the leading family in New York and take on that mantle himself. He was the one behind Sollozzo, not Tattaglia, and ultimately it was Barzini's people who were establishing the drug trade in New York. This leads to the likelihood that had Vito gone along with the original idea to get into the drug business, that Barzini would allow Sollozzo to set things up, and then kill him to gather more power. This would not have caused a war because no one was beholden to Sollozzo, and the drug trade would have continued without the need for paying Sollozzo a dime.

When Vito refused to get into the business, Barzini saw his chance to have Vito assassinated, shatter the Corleones, and
let Sollozzo take the blame. Either way Barzini would win.
And either way Sollozzo was going to wind up dead. In esence, therfore Michael did Barzini a favor by killing Sollozzo and maneuvering the Corleones and the Tattaglias to fight among themselves.

What I am wondering here is how did it escape Vito, Santino and Tom that it was Barzini pulling the strings, and not that pimp Tattataglia for such a long time.