Werte you alivw then? If you were you would know that most did not believe the government lies. The CIA has always been suspected.
I was alive then. Were you?
Early on, many believed JFK was a victim of conservatives unhappy with his civil rights policy or his policy of appeasement toward Communist countries. This notion was promoted in the media and in books such as Dallas, Public and Private by Warren Leslie (New York: Avon, 1964). This viewpoint is still promoted in books like Dallas 1963 by Bill Minutaglio and Steven Davis (New York: Twelve, 2013). I haven't yet read Nut Country: Right Wing Dallas & the Birth of the Southern Strategy by Edward Miller (Chicago: University of Chicago Press, 2015) but I assume it promotes the same viewpoint.
Many in the conservative media thought that the Soviets or Cubans were behind the assassination because Oswald was a Communist and Jack Ruby had apparently also been one when he was younger. In an article in the John Birch Society publication American Opinion, Revilo Oliver suggested that JFK was killed because he was about to "turn American" and purge the Deep Staters from his administration, withdraw from the United Nations and take a hard line against Communism. A more sober viewpoint is expressed in Carlos Bringuier's Red Friday: November 22, 1963 (Chicago: Hallberg, 1969) which emphasizes Oswald's Cuban connections.
I don't recall hearing conspiracy theories involving the CIA until around the end of the sixties.