In Assassin's Creed III, the historical story begins in 1754.
The game opens with Haytham Kenway in colonial Boston and New York during the early stages of the French and Indian War. This opening is set decades before the Declaration of Independence and introduces the conflict between the Assassins and Templars through Haytham’s perspective.
After Haytham’s opening sequence, the story shifts to Ratonhnhaké:ton, also known as Connor, whose life is shaped by the escalating struggle between the British Crown, colonial revolutionaries, Native nations, and the Templar Order. The main Revolutionary War period arrives later, but 1754 is the starting year for the historical narrative.
The year 1775 is a common alternative because it marks the outbreak of the American Revolutionary War and is central to the later campaign. It is not, however, the beginning of Assassin's Creed III’s historical story.