Little Big Man, written in 1964, by Thomas Berger is not a true story. The book with stories of Jack Crabb's adventures in the West is based on a compilation of many different journals, diaries, and other writings of people who did live in the old West. However, Berger used these stories and journals to create characters and stories that are entertaining and created a character in Crabb that enjoyed real life adventures with many historical figures.
Crabb's travels brought him face to face with General George Armstrong Custer, Wild Bill Hickock, Wyatt Earp, and Buffalo Bill. His adventures allow him to share historical accuracy of certain events, but are a conglomeration of many different people's experiences with these people.
In Forrest Gump we see a similar experience in which the protagonist experiences many of the great events of the 1960s to the present. In Gump, Forrest experiences many important events and meets historical figures. In Gump, too, he is a collection of many different people who did have these life experiences.
Crabb and Gump both witnessed amazing things; both Crabb and Gump, though, are fictional people.