Lemnitzer and the Joint Chiefs worked out a complex deception:

An aircraft at Elgin AFB would be painted and numbered as an exact
duplicate for a civil registered aircraft belonging to a CJA proprietary
organization in the Miami area. At a designated time the duplicate
would be substituted for the actual civil aircraft and would be loaded
with the selected passengers, all boarded under carefully prepared
aliases. The actual registered aircraft would be converted to a drone
[a remotely controlled unmanned aircraft]. Take off times of the drone
aircraft and the actual aircraft will be scheduled to allow a rendezvous
south of Florida.

From the rendezvous point the passenger-carrying aircraft will
descend to minimum altitude and go directly into an auxiliary field at
Elgin AFB where arrangements will have been made to evacuate the
passengers and return the aircraft to its original status. The drone
aircraft meanwhile will continue to fly the filed flight plan. When over
Cuba the drone will be transmitting on the international distress
frequency a "May Day" message stating he is under attack by Cuban
MiG aircraft. The transmission will be interrupted by destruction of the
aircraft, which will be triggered by radio signal. This will allow ICAO
[International Civil Aviation Organization radio stations in the Western
Hemisphere to tell the U.S. what has happened to the aircraft instead
of the U.S. trying to "sell" the incident.

Finally, there was a plan to "make it appear that Communist Cuban
MiGs have destroyed a USAF aircraft over international waters in an
unprovoked attack." It was a particularly believable operation given the
decade of shoot downs that had just taken place.

Gee, does this seem recently familiar.