I'm sure the 'dogs of war' tried.
In '60 Eisenhower green-lit an invasion plan by the CIA (Dulles) in response to the nationalisation of Esso, Standard Oil and Shell in Cuba. Does this sound familiar? (https://www.jfklibrary.org/JFK/JFK-in-History/The-Bay-of-Pig...)
It's election year. Kennedy was elected in '60 and a key part of that was equalising the 'missile-gap'. There was no missile gap. US had 100 times the capability of USSR. (https://en.wikipedia.org/wiki/Cuban_Missile_Crisis#Balance_o...)
In '61 Kennedy didn't provide ^air support^ for Operation Mongoose organised by Lansdale. (https://en.wikipedia.org/wiki/Cuban_Project) Dulles is fired as head of the CIA.
In October '62, the US B team of Generals (Joint Chiefs of Staff) LeMay, Lansdale, Anderson, Anderson, Shoup and Wheeler were being pushed for implementing the first strike over Russian (LeMay) and invading Cuba again (Lansdale). (https://govbooktalk.gpo.gov/2012/10/18/hawks-vs-doves-the-jo... and https://en.wikipedia.org/wiki/Cuban_Project) The time clock of the missile crisis, shows the operational nature of the CIA. (http://nsarchive.gwu.edu/bayofpigs/chron.html)
Cooler heads prevailed. Khrushchev and Kennedy negotiated secretly, while the military of both sides maintained their cool. Just as well. It's now known that Cuba was in the possession of ^tactical^ nuclear weapons. So without any control from the USSR, field commanders ^could^ have deployed them if Cuba was invaded. (https://en.wikipedia.org/wiki/Cuban_Missile_Crisis#Post-cris...)
In '63, JFK was assassinated. A year after that Khrushchev was rolled. The change of US political direction allowed the war footing to escalate, ever since.
Lansdale, LeMay, Dulles, Nixon, the CIA and US arms and resource companies all had great careers in the post '63 era. [0]
[0] The inference here is you can find potential conspirators that lead to 22 November 1963. The same names appear again and again in the "Assassination Records Review Board: Files of Douglas P. Horne" (http://www.archives.gov/research/jfk/review-board/horne-file...)