If Oswald was the assassin and acted alone, then what was his plan after the assassination? His best move likely would have been to surrender at the scene and declare that shooting Kennedy was a revolutionary act on behalf of the oppressed. He could then angle to get exchanged one day in a Cold War spy swap, with Cuba his destination of preference.
It is hard though to discern in Oswald's movements that grim day in Dallas any plan of escape other than to leave the immediate scene. It is not at all clear how Oswald expected to then get to Cuba. His movements and actions instead suggest a sense of panic as if things did not go as expected. Did Oswald extemporize because he was betrayed and stranded by one or more supposed confederates?
There is also the enduring mystery of an apparent Oswald imitator in Mexico City during his visit there. This strongly suggests conspiracy, at least by the CIA to use Oswald as a lure to draw interest from Cuban intelligence. Plausibly, there was a parallel assassination conspiracy that used and set up Oswald to take the fall.
It’s important to remember that Oswald was a 10th grade drop out, a bad student, and while not stupid exactly he was not real bright either. At the age of 10, he scored 103 on an IQ test. Several years later he did better, managing a 118 after being admitted to Youth House in New York. However he was antisocial, an under achiever, disruptive and withdrawn. At 14 he was diagnosed with “personality pattern disturbance.” He was hardly the type anyone would want as a confederate in murder or espionage. Likely he had no real plan of escape. It is noteworthy that he was the ONLY employee of the Texas Schoolbook Depository that left early that day, and did so on his own initiative, without telling anyone he was leaving.
Furthermore when traffic jammed he ditched the bus he was in and hailed a cab. This was unusual for Oswald because he was such a miser. He was desperate to get home. He had the cabbie drive PAST his residence, an obvious attempt to make sure the coast was clear before walking the three blocks BACK to the boardinghouse. There he grabbed a gun and a jacket to hide it in. Thus his desperation to get there. He knew the cops would be after him.
Oswald was the classic example of the “lone nut.” Nuts don’t reason things out. He was smug and uncooperative with the police. In his nutty mind he may have thought the Castro regime would somehow bail him out. Who knows what he was thinking when planning to shoot the President.