One way I could see it happening is for the Stamp Act Crisis to spiral out of control. Perhaps the British double down and send troops to protect their stamp distributors' properties from mobs. Violence continues, and presumably it would peak in Boston or some other major settlement, and the British may send more troops to pacify the city. Might be an analog to some of the Intolerable Acts follow (like the [X City] Port Act, Administration of Justice Act, Quartering Act). From there, things would proceed much as they did in 1774-75 -- militias mustering, powder alarms, the whole thing.
As for the war itself, I could see it being a regional thing. OTL the various crises prior to the outbreak of war in 1775 helped tie together the revolutionaries across the continent -- got them talking, organizing opposition, building closer relationships. Getting the war war going a decade early means that rebellion is going to be more concentrated in one part of the colonies and less so otherwise -- likely on a north-south axis. It'll be weaker and, probably, more easily snuffed out.