Elisha Hinman was born in Stonington, Connecticut, on March 9, 1734, the son of a merchant marine captain. He followed into his father's service at an early age and at the age of 19 commanded his own brig in the West Indies trade. In 1776, Elisha Hinman was commissioned a Lieutenant in the Continental Navy and assigned to the brig 'Cabot' under Captain John B Hopkins. In this capacity he accompained the New Providence expedition of Commodore Esek Hopkins and was present during the embarrasing encounter with HMS "Glasgow" on April 6, 1776. He nonetheless acquitted himself well and assumed command of the 'Cabot' the following August. On October 10, 1776, Elisha Hinman received promotion to Captain, being 20th on the Seniority list, and succeeded John Paul Jones as Commander of the 'Alfred', a converted merchantman and one of the nations earliest warships.
In 1779 a new frigate was commissioned on the Connecticut River, but was to heavy to cross the bar into Long Island Sound. Elisha Hinman figured out a way to get the 'Trumbull' out.
In 1781 he was captain of the "Marquis de LaFayette", a brig which he sailed as a privateer for owner Thomas Mumford, who was possibly an in-law.