I don't know of any reason why we would doubt they existed. Chen Shou, the author of the most important primary source for the period, the Sanguozhi or Records of the Three Kingdoms, lived during the Three Kingdoms period and his biography in the Book of Jin states that he was first an official of the Shu state and later served Jin after unification. His history is widely regarded as credible (by the likes of Rafe de Crespigny, Mark Edward Lewis, and Etienne Balasz) and no alternative chronology of the period exists that I'm aware of. Furthermore some important events and people of the era are verified by other evidence- for example, the literal tomb of Cao Cao, the warlord who laid the foundations for the Wei state, was just recently identified in Henan.

You may be confused by the fact that, besides the contemporary and near-contemporary historical sources that record the era, there is also the much later novel Romance of the Three Kingdoms by Luo Guanzhong, which draws on Chen Shou's history but ups the interpersonal drama, adds in unbelievable martial feats and incorporates some scenes with supernatural elements (including, for example, a Buddhist monk talking down the angry ghost of Guan Yu). This novel is a fictionalization of actual historical events. You may have heard that much of the Romance of the Three Kingdoms was not true and gotten the mistaken impression that the Three Kingdoms themselves were fictional to begin with.