The ship was one of the Coventry class, designed by Sir Thomas Slade as a development of based on HMS Lyme, "with such alterations as may tend to the better stowing of men and carrying for guns."

The Navy's choice of this name followed a trend initiated in 1748 by John Montagu, 4th Earl of Sandwich, in his capacity as First Sea Lord, of using figures from classical antiquity as descriptors for naval vessels.

[5][6] She was also built with broad and heavy masts, which balanced the weight of her hull, improved stability in rough weather and made her capable of carrying a greater quantity of sail.

After receiving stores, guns and crew she was out to sea in late January 1759 under the command of Captain John Tinker, and was assigned to the British squadron blockading the French-held port of Dunkirk.

In a two-hour action on 31 October 1762, Argo and the Edgar-class fourth-rate 60-gun HMS Panther captured the Spanish galleon Santísima Trinidad, loaded with cargo valued at $1.5 million.