Answer:
The United States routinely conducted U-2 reconnaissance overflights of Cuba after Castro took power, and one overflight took pictures that under detailed analysis were determined to be launchers and support equipment for nuclear missiles. The estimated flight time from Cuba to Washington was less than 30 minutes, though the time to Florida would've been a lot less. Though the sites were considered not be yet operational, it was felt that they were within days of being completed, and Kennedy was immediately informed of the threat. The presence of nuclear weapons in Cuba represented a fundamental shift in Soviet doctrine and a major threat in the Western Hemisphere.
Not known at the time but disclosed later on after the fall of the Soviet Union was the fact that battlefield Tactical Nukes were also in Cuba at the time. Had Kennedy decided on an invasion, there is no question those would've been used, and I wouldn't be sitting here telling you how it turned out decades later.