Born in 1766 in Algiers, where his father was Consul general, Bayntun joined the navy at a young age and received his lieutenancy at just seventeen on 15 April 1783. When war broke out with Revolutionary France in 1793, Bayntun was sent to the West Indies under Admiral Sir John Jervis and, after taking part in the capture of Martinique, he was given command of the sloop . Bayntun was also present during the invasion of Guadeloupe and on the 4 May 1794, he was appointed post captain of HMS "Undaunted", the former French frigate, "La Bienvenue", captured during the Battle of Martinique.