@regular john one thing to note in CIA hypotheses is that they largely rely on modern understandings of the CIA's reach and power. In 1963, the CIA mostly had a reputation as a clumsy organisation that bungled as many things as it achieved. There had been a few successful ops that overthrew governments, but the agency was full of miscalculations and leaks, as well as several double agents. Later in the 60s into the 70s we see the CIA become a bit more effective as it shifts a lot of its energy to Central and South America (following various failures in Asia), a project that really takes off in the 70s and 80s. Most of our modern understanding of the CIA as the puppet masters of the world come from the things they did in the 80s. By then, several countries had felt their touch.
I only say all that to say that the CIA in 1963 would likely have not been able to contain news of their participation in an event like the assassination of Kennedy. It's not impossible that a small group of agents could have participated in it as a side project, but the agency was so incredibly incompetent and bush league in '63 that those agents would have had to have very specific motives, which are generally hard to find. A lot of lore, much of it issuing from the Oliver Stone film, makes it seem like JFK and the CIA had an antagonistic relationship, but in reality Kennedy was very generous to them and supported their mission quite a bit. Certainly more than his predecessor Eisenhower. Arguably much too much as they set about toppling regimes for him much more successfully than they managed in Laos or Cuba.
There are other institutional actors that more plausibly could have been involved from the mob to the Soviets to the Cubans to the FBI. Or it could've just been Oswald, influenced by several actors, though maybe not acting on their behalf per se. His own murder so soon after being taken into custody means we're left mostly to speculate. When you situate the assassination in the context of many other political assassinations and attempted assassinstions that occurred, it begins to look a bit less unique. After McKinley was shot at the start of the 20th century, most of his successors also fended off assassination attempts. William Howard Taft nearly got shot. Teddy Roosevelt was famously shot during a campaign speech. Attempts were made on Hoover, FDR, and Truman. Malcolm X was killed a couple years after Kennedy. MLK and Bobby Kennedy were murdered in '68. Thereafter, there were plots or attempts on Nixon, Ford, Carter and of course Reagan who was shot. The 20th century was still a very violent time with a lot of conflicting politics and loyalties. The growth of the modern surveillance state, more expansive mental health services, and a more effective and better funded Secret Service have probably been most of the reason for it being less common today. Because of that it's hard to project ourselves back to that time, but realistically a small group of committed people or even a lone actor could feasibly have carried out an assassinstion of a President. In many ways, the conspiracies help to preserve the myth of an all powerful state (or shadow state) that sees all, knows all and can get away with anything, which encourages people both at home and abroad to believe that resistance is futile. At this point, who killed Kennedy and why is irrelevant except as a thought experiment. What's more interesting is what purposes the stories of his death serve when you look into the worldview they incentivize belief in. I would not at all be surprised if the rumors of CIA involvement were started by the CIA.