Supposedly, in Mob "lore," you have to serve a long apprenticeship (as Christopher did in "Sopranos") and then, if you're lucky, they tap you on the shoulder and tell you to kill someone for them. Then you get "made" in the ceremony with the burning saint's card, finger-pricking, etc.
As a practical matter, there's no such rule because a Don can make whomever he wants, for whatever reasons. Some follow that kind of ceremony, others don't. Fat Vinny Teresa, in his book, "My Life in the Mob," said that the Boston outfit under Raymond Patriarca never had a formal ceremony: "They just called you to the office one day and told you that you were in." Salvatore (Bill) Bonanno was being groomed by his father as the next Don, and he never mentioned being formally made. John Gotti served as a crew chief in the Gambinos long before he was formally made. Jimmy Burke functioned as a crew chief in the Luccheses and he didn't even have a drop of Italian blood.