No, the hero himself does not have a specific prototype in real life. His features are rather taken from many case histories of people with convulsive-impulsive mental disorders. But the scene with the Forrest Gump race is really based on real events. Luis Michael Figueroa ran from New Jersey to San Francisco in 1982. So he decided to support the Cancer Society. It was he who said: "I just put one foot in front of the other," which was then transferred to the film.
The ceremony with the awarding of the Medal of Honor was also real. True, they handed it, of course, not to Forrest Gump, but to Sammy L. Davis. The ceremony took place on November 19, 1968, and was presented by US Vice President Lyndon Johnson. In the frame, the head of Tom Hanks was "attached" to the body of Davis using modern technology. As a result, the footage turned out to be very convincing.