Tom had been consigliere for only 3 months. He took over when Genco died on the evening of Connie's wedding.

Solozzo probably would have moved against Vito after Vito said no, even if Genco had still been consigliere. Tom thought of himself as an unfit consigliere, and that Genco would have smelled a rat, after he learned that Sonny had been murdered. But, I'm thinking that Genco would have figured that Solozzo, as a Sicilian, would take Vito's "no" as a personal affront--depriving him and his people of a living--and would have predicted that Sol would move against him.