Salmon was born in Whitehaven, Cumberland, England in October or November, 1775 as Robert Salomon; he was christened on 5 November 1775 in Whitehaven. His father, Francis Salomon, was a jeweler. The young Salmon clearly studied the work of Dutch marine painters of the 17th century, the Italian painters of "vedute", and the work of Claude Lorrain, but little else is known of his early training. His earliest known works, "Two Armed Merchantmen Leaving Whitehaven Harbor" and "The ‘Estridge’ Off Dover" are dated 1800; the first work he exhibited at the Royal Academy was in 1802.