The Soviets saw him as too incompetent to be an agent. They tried.Lets say that the night Lee Harvey Oswald is supposed to be assassinated, Jack Ruby decides to cancel his shooting, or instead misses, or the doctors manage to save Lee Harvey Oswald's life.
There are many theories as to what happened, so we will examine two of them. If Lee Harvey Oswald said-
1. The Soviet Government paid him to kill Kennedy for what happened with the Cuban Missile Crisis
Oswald was a loner with delusions of becoming a historically significant figure that'd be remembered for generations, and with a need to be unique and the center of attention. He had no connection with the Mafia besides, nor do I believe would ever consider working for something that'd symbolize the worst part of Capitalism to the Communist mind.2. The Mafia was responsible