The event that led to the start of the American War of Independence was the imposition of the Stamp Act in 1765, which incited anger among colonists against British taxation without representation. Tensions escalated with events like the Boston Tea Party in 1773 and the Intolerable Acts in 1774. The combination of these injustices, along with calls for freedom and self-governance, ultimately culminated in the outbreak of war in 1775, marking a significant turning point in American history.