The question of who fired the first shot in the American Revolutionary War is famously associated with the battles of Lexington and Concord on April 19, 1775. The phrase "the shot heard 'round the world" refers to this event.
Historically, it is often stated that both sides fired at the same time, and there is some ambiguity as to who actually fired the first shot. The British troops were marching to seize colonial military supplies, and the American colonists were gathered to resist them. As such, the correct interpretation of the situation suggests that no one definitively knows who fired first, as both sides were involved.
So, the answers could be “Both sides shot at the same time” or “No one knows” depending on the perspective you take.