Born in Philadelphia, Pennsylvania, Godon entered the Navy in 1819 as a midshipman, and, after serving at sea in various parts of the world, was promoted passed midshipman in 1827, and to lieutenant in 1836. He served in the , flagship of Commodore Isaac Hull's Mediterranean Squadron from 1839 to 1841. Godon was actively employed during the Mexican–American War, in command of the bomb vessel at the reduction of Veracruz in 1847.