Inglis was born c. 1731, the fourth son of Sir John Inglis and his wife Anne, the daughter of Adam Cockburn. He embarked on a naval career, at first joining the 40-gun under Captain George Brydges Rodney, in 1745, and the next year went with Rodney to the 60-gun . Rodney carried out several successful cruises, capturing four ships from a French convoy in June 1747, and fighting under Rear-Admiral Edward Hawke at his clash with Desherbiers de l'Etenduère's fleet at the Second Battle of Cape Finisterre on 25 October 1747. Inglis saw action on both of these occasions. "Eagle" was heavily engaged with the French 70-gun "Neptune" in the latter engagement and suffered considerable damage. She was paid off in August 1748 on the conclusion of the peace, and Inglis was left without a ship. He remained unemployed until 1750, when he joined the 50-gun , at that time under the command of Captain Francis Holburne. Inglis's biographer, P. K. Crimmin noted that like Inglis, Holburne was a lowland Scot, and that Inglis may have been benefiting during this time from a network of patronage that included John Cockburn, Inglis's uncle and a Lord of the Admiralty between 1727 and 1732 and again during 1742 and 1744, and Sir John Clerk, a friend of the family with considerable political influence.