Yes, Tom said "maybe we shouldn't get Mike too involved." And Sonny said, "The old man would have my head..." if Michael got involved. And, when Michael said he was going to visit Vito in the hospital, Clemenza proposed that Michael go alone because "Solozzo knows he's a civilian." All reinforcing that Michael explicitly wasn't part of the family business to that point.

What changed? Two things:

First, when Michael saw that Vito was unprotected in the hospital because his bodyguards had been arrested, he said, "I'm with you now, Pop." Many people here believe that it was Michael's turning point--that he was now part of the family business, not simply that he was physically with Vito. Second, when McCluskey broke his jaw, Michael knew he was now personally involved. And finally: Michael was the only logical assassin for Solozzo: Fredo'd had a nervous breakdown and, as Tom said, "Solozzo wouldn't let you near him if he had ten police captains. Besides, as acting head of the family, you can't be risked."

To your point about if it was always planned for Michael to be part of the family: that's a good question. Was Michael always destined to be the Don? Was he destined for a life of crime? In the novel, Vito says, more than once, "a man has but one destiny." He didn't say it about Michael explicitly. In the novel, Clemenza, driving Kay home from Connie's wedding, says that Michael will take over the family business. In the flashback scene at the end of II, Tom tells Michael that "your father and I have made plans for you."