Hailing from New Jersey, Kenwith had a long career on Broadway as well as in regional theater before turning to television. On Broadway, he was an assistant stage manager and performer in the original production of I Remember Mama, which ran for 713 performances between 1944 and 1946 and marked Marlon Brando's Broadway debut. Kenwith later produced the original Broadway production of Me and Molly, which ran for 156 performances in 1948 and featured David Opatoshu in the cast. After Broadway, Kenwith produced and directed 65 plays for Princeton University's McCarter Theater. Among the performers he worked with during this time was Lucille Ball, who later tapped Kenwith as a director on her show, Here's Lucy.