Answer by taking a quote from the following article:

Tierney was born on November 19, 1920 in Brooklyn, New York, the daughter of Howard Sherwood Tierney and Belle Lavinia Taylor. She was named after a beloved uncle, who died young. She had an elder brother, Howard Sherwood "Butch" Tierney, Jr., and a younger sister, Patricia "Pat" Tierney. Their father was a successful insurance broker of Irish descent, their mother a former physical education instructor.

In Tierney's first role on Broadway, she carried a bucket of water across the stage in What a Life! (1938). A Variety magazine critic declared, "Miss Tierney is certainly the most beautiful water carrier I've ever seen!" She also worked as an understudy in The Primrose Path (1938).  The following year, she appeared in the role of Molly O'Day in the Broadway production Mrs. O'Brien Entertains (1939). The New York Times critic Brooks Atkinson wrote, "As an Irish maiden fresh from the old country, Gene Tierney in her first stage performance is very pretty and refreshingly modest." That same year, Tierney appeared as Peggy Carr in Ring Two (1939) to favorable reviews. Theater critic Richard Watts, Jr. of the New York Herald Tribune wrote, "I see no reason why Miss Tierney should not have an interesting theatrical career - that is, if cinema does not kidnap her away."  Tierney's father set up a corporation, Belle-Tier, to fund and promote her acting career. Columbia Pictures signed her to a six-month contract in 1939. She met Howard Hughes, who tried unsuccessfully to seduce her. From a well-to-do family herself, she was not impressed by his wealth. Hughes eventually became a lifelong friend.  After a cameraman advised Tierney to lose a little weight, she wrote to Harper's Bazaar magazine for a diet, which she followed for the next 25 years. Tierney was initially offered the lead role in National Velvet, but production was delayed. When Columbia Pictures failed to find Tierney a project, she returned to Broadway and starred as Patricia Stanley to critical and commercial success in The Male Animal (1940). In The New York Times, Brooks Atkinson wrote, "Tierney blazes with animation in the best performance she has yet given". She was the toast of Broadway before her 20th birthday. The Male Animal was a hit, and Tierney was featured in Life magazine. She was also photographed by Harper's Bazaar, Vogue, and Collier's Weekly.  Two weeks after The Male Animal opened, Darryl F. Zanuck, the head of 20th Century Fox, was rumored to have been in the audience. During the performance, he told an assistant to note Tierney's name. Later that night, Zanuck dropped by the Stork Club, where he saw a young lady on the dance floor. He told his assistant, "Forget the girl from the play. See if you can sign that one." It was Tierney. At first, Zanuck did not think she was the actress he had seen. Tierney was quoted (after the fact), saying: "I always had several different 'looks', a quality that proved useful in my career."

Did she star in any musicals?
she appeared in the role of Molly O'Day in the Broadway production Mrs. O'Brien Entertains (1939