Nowhere does it say that Carlo was a made man. And, even if he were, it would have been considered a family matter, not subject to some Mob BS rule that probably wasn't enforced anyway. Besides, Sonny was acting Don--and who was going to say boo to him?
I think I guessed that he was a made guy due to Michael moving him up once he became boss. He must have been made sometime between Sonny’s murder and Michael becoming don. Or as you said, it was a family matter and Carlo had no respect.
Michael said, "You're going to be my right hand man in Nevada." The novel says Carlo grew up in Nevada. Doesn't necessarily mean he was made--doesn't necessarily mean he wasn't made.
But, you raise an interesting point: Was anybody in the Corleone Family actually made? No depiction or mention of an actual "making" ceremony is shown or mentioned in the film or in the novel. Vito became a Don by killing Fanucci, taking over his local rackets, and expanding them via the "olive oil business." Clem and Tess were his trusted associates. Sonny, Fredo and Michael were sons. Granted, the Trilogy is fiction. But, I doubt Puzo and Coppola would have passed up an opportunity to show a "making" ceremony if they thought it was necessary or even relevant to the story. About the closest we see is Clem kissing Michael's hand at the very end and saying, "Don Corleone." Nice dramatic touch, period.
As I mentioned earlier, there's no ironclad rule that I know of that says everyone in every Mafia family has to be made--depends on what the Don wants to do. I think that was especially true in the era when GF takes place.
