Hunt was born on 23 February 1824 at Fort Howard in Green Bay, Wisconsin. He was the son of Samuel Wellington Hunt, his brother being fellow general Henry Jackson Hunt. He entered the United States Military Academy in 1843 and graduated in 1847, ranking 33rd out of 38. Serving in the 4th U.S. Infantry Regiment; after being promoted to captain Hunt served as the commander of the U.S. force on San Juan Island in 1859. Hunt was relieved from duty on San Juan Island in April 1860 by George Pickett.