Cook was born in 1903 in San Francisco, California, the son of Elisha Vanslyck Cook Sr., a pharmacist, and grew up in Chicago. He first worked in theater lobbies selling programs, but by the age of 14 he was already performing in vaudeville and stock. As a young man, he traveled and honed his acting skills on stages along the East Coast and in the Midwest before arriving in New York City, where in 1926 he debuted on Broadway in Hello, Lola. Some other Broadway productions in which Cook performed were Henry-Behave (1926), Kingdom of God (1928), Her Unborn Child (1928), Many a Slip (1930), Privilege Car (1931), Lost Boy (1932), Merry-Go-Round (1932), and Chrysalis (1932). Then, in 1933, Eugene O'Neill cast him in the role of Richard Miller in his play Ah, Wilderness, which ran on Broadway for two years. Cook continued to appear on stage during the remainder the 1930s; and although his acting career after that focused increasingly on films and then on television roles, he periodically returned to Broadway, where as late as 1963 he performed as Giuseppe Givola in Bertolt Brecht's play The Resistible Rise of Arturo Ui.