I think the first step would be a warning of back down or else and then we'll go from there.
Here's just a quick recap from wiki for the sake of summation:
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When this was reported to President John F. Kennedy, he convened a meeting of the nine members of the National Security Council and five other key advisers, in a group that became known as the Executive Committee of the National Security Council (EXCOMM). During this meeting, Kennedy was advised to carry out an air strike on Cuban soil in order to compromise Soviet missile supplies, followed by an invasion of the Cuban mainland. After careful consideration, he chose a less aggressive course of action, in order to avoid a declaration of war. After consultation with EXCOMM, Kennedy ordered a naval "quarantine" on 22 October to prevent further missiles from reaching Cuba.[url=https://en.wikipedia.org/wiki/Cuban_Missile_Crisis#cite_note-6][6][/url] By using the term "quarantine", rather than "blockade" (an act of war by legal definition), the United States was able to avoid the implications of a state of war.[url=https://en.wikipedia.org/wiki/Cuban_Missile_Crisis#cite_note-uslegalcaseblockadeofcuba-7][7][/url] The US announced it would not permit "offensive" weapons to be delivered to Cuba and demanded that the weapons already in Cuba be dismantled and returned to the Soviet Union.
After several days of tense negotiations, an agreement was reached between Kennedy and Khrushchev. Publicly, the Soviets would dismantle their offensive weapons in Cuba and return them to the Soviet Union, subject to United Nations verification, in exchange for a US public declaration and agreement to not invade Cuba again. Secretly, the United States agreed with the Soviets that it would dismantle all of the Jupiter MRBMs which had been deployed to Turkey. There has been debate on whether Italy was also included in the agreement. While the Soviets dismantled their missiles, some Soviet bombers remained in Cuba, and the United States kept the naval quarantine in place until 20 November 1962.[url=https://en.wikipedia.org/wiki/Cuban_Missile_Crisis#cite_note-uslegalcaseblockadeofcuba-7][7][/url]
But from what I understand pretty much everyone in that room was advising a bombing and invasion of Cuba, and later pretty much everyone in that room was calling for Kennedy to launch nuclear bombs on the Soviet Union. Those tense negotiations were as tense as it gets with people on our side telling Kennedy he's sending us to our deaths if we don't launch.
Everyone in that room agreed we had the justification we needed to bomb and launch a full scale invasion of Cuba. The ONLY reason we didn't is because of the threat of nuclear war, and that reason was only reason enough for Kennedy. The rest thought it was past that.
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To think the usa would have been justified in a full invasion and occupation of Cuba is asinine.
I guess every one of Kennedy's advisers were also asinine. If someone ever puts a gun to your head, you also would be asinine if you believe you have the justification to do something about it.
So, yes. I believe we had the justification we needed to take whatever action we decided to take with Cuba. Whether we act or don't, the justification was there.