I believe for Michael waited a year for two reasons, Apollonia died, and Michael needed to take care of the family and during that time he developed his Don like character more.

"Well you just do what I tell you to do! Goddamn it! If I had a wartime consiglieri -- a
Sicilian -- I wouldn't be in this shape! Pop had Genco -- look what I got." - Sonny Corleone