She made her film debut at the age of nine in Westward Passage (1933), and appeared that same year in a credited but nearly wordless supporting role as the young Dancer Fanny Bridges in Cavalcade, which won the Academy Award for Best Picture. Over the next few years, she played uncredited supporting roles in such films as Little Women (1933) and Anne of Green Gables (1934). She next played the role of Mary Tilford in the 1936 film adaptation of Lillian Hellman's 1934 stage play The Children's Hour. Renamed These Three, the film told the story of three adults (played by Miriam Hopkins, Merle Oberon, and Joel McCrea) who find their lives almost destroyed by the malicious lies of an evil, attention-seeking child. For her role as that child, Granville was nominated for an Academy Award for Best Supporting Actress, then the youngest person to be nominated for that award. Despite this success, and although she continued to work, the next few years brought her few opportunities to build her career.