George Murray was born in Chichester in January 1759. His father was Gideon Murray, Alderman of that city. He began his naval career at the age of 11, when he was entered in the books of Captain Francis Banks's , which was serving in the Mediterranean, as a captain's servant. His proper service in the navy probably began in 1772, when he joined , the flagship of Commodore Molyneux Shuldham, for service on the Newfoundland Station. He then transferred to the flagship of John Montagu, the 50-gun , and again in time to join Sir Peter Parker's flagship for the attack on Sullivan's Island on 28 June 1776. He moved into after this and continued to serve with Parker along the North American coast, participating in the occupation of Rhode Island in December 1776. After receiving favourable reports of his conduct, Vice-Admiral Lord Howe requested Murray's services and he was transferred to . Murray went on to see action in Howe's campaigns to disrupt the French fleet under comte d'Estaing in the summer of 1778.