1590s in the literal sense; c.1600 in the figurative sense, from progress, n.. OED says the verb was obsolete in English 18c. but was reformed or retained in America and subsequently long regarded in Britain as an Americanism. Related: Progressed; progressing.

late 14c., "a going on, action of walking forward," from Old French progres (Modern French progrès), from Latin progressus "a going forward," from past participle of progredi (see progression).In early use in English especially "a state journey by royalty." Figurative sense of "growth, development, advancement to higher stages" is from c.1600. To be in progress "underway" is attested by 1849. Progress report attested by 1865.