Michael was the only one who strategiced - Sollozzo killing Vito is the key, the Corleones can't wait - devised the brilliant plan and carried out successfully the murders of Sollozzo and the New York Police captain pretty much single handed

Michael did all that in spite of Tom's “nobody has ever gunned down a New York police captain Never!

If that was not proof for Tessio that Michael was “more than qualified to be the new don” confront Barzini, stop Barzini encroaching into Corleone territories and win

Well, Don Barzini and Don Tessio! both were slipping that Michael would fall for this transparently ill-conceived charade