My Dad always believed it was Cuba that ordered the hit but our government couldn’t tell us because it would lead to war with Russia.
The “Cuba” claim was the CIA’s original cover story—they sent a fake Oswald to Mexico to the Cuban embassy as part of that ruse.
That cover story was given to LBJ, and he in turn used it to convince Earl Warren that the Warren Commission had to blame everything on the patsy Oswald.
It was a good cover story given the many CIA assassination attempts on Castro—certainly cause for retaliation—but Castro did not have the ability to carry out such a plot.
In addition the Russians were involved in nuclear negotiations with JFK at the time and would not want him assassinated (and Castro did as he was told by the Russians).