score:10
J. Edgar Hoover knew perfectly well that organized crime existed before 1957. In the 1940's he had been known to sit at the same table in upscale clubs with known underworld figures like Meyer Lansky (source: J. Edgar Hoover: The Man and the Secrets, by Curt Gentry).
He preferred to not acknowledge the mafia's existence so he would not be obliged to assign FBI agents to build cases against them. He chose to assign his agents to cases like unorganized interstate crime ("Pretty Boy" Floyd, John Dillinger, "Baby Face" Nelson), infiltrating the Communist party, and spying on and harassing civil rights leaders. It was only the blatant publicity of the Apalachin Meeting, after it was raided by state and local police, that forced the FBI director to admit that the mafia was an actual organization.
Upvote:5
David Carter's "Stonewall: The Riots That Sparked the Gay Revolution" actually discusses this. Not only did the mafia run many of the gay bars in New York and other places, but they also frequently blackmailed prominent people who frequented them. One blackmail ring was broken up and it was later discovered that they were blackmailing US generals and Senators. The book also interviewed male prostitutes that had attended mafia run events that Hoover attended while dressed as a woman. (As we know now, he also had a long-time male romantic partner.)
So it would be very likely that he was very aware of the mafia but they also had lots of blackmail material on him, which prevented he from acknowledging their existence until he absolutely had to.