Dawes was born in Boston, Massachusetts, on April 6, 1745, to William and Lydia Dawes (née Boone), and baptized at Boston's Old South Church. He became a tanner and was active in Boston's militia. On May 3, 1768, Dawes married Mehitable May, the daughter of Samuel and Catherine May (née Mears). The Boston Gazette noted that for his wedding, he wore a suit entirely made in North America. At the time, Whigs were trying to organize a boycott of British products to pressure Parliament into repealing the Townshend Acts.
On April 8, 1768, Dawes was elected as a member of the Ancient and Honorable Artillery Company of Massachusetts. He was appointed as the Company's second sergeant in 1770. When the Company was revived in 1786, after becoming dormant during the American Revolution, he was appointed as the Company clerk. His father, William Dawes Sr., was also a member of the Company.
It is likely that in September 1774, Dawes was instrumental in helping Boston's militia artillery company secure its four small cannons from British army control. The Massachusetts Provincial Congress certainly sent word to him in February 1775 that it was time to move two of those weapons out of Boston.
Dawes was assigned by Doctor Joseph Warren to ride from Boston to Lexington, Massachusetts, on the night of April 18, 1775, when it became clear that a British column was going to march into the countryside. Dawes's mission was to warn John Hancock and Samuel Adams that they were in danger of arrest. Dawes took the land route out of Boston through the Boston Neck, leaving just before the British military sealed off the town.
Also acting under Dr. Warren, Paul Revere arranged for another rider waiting across the Charles River in Charlestown to be told of the army's route with lanterns hung in Old North Church. To be certain the message would get through, Revere rowed across the river and started riding westward himself. Later, Henry Wadsworth Longfellow's historically inaccurate poem "Paul Revere's Ride" would focus entirely on Revere, making him a composite of the many alarm riders that night.