Until the late 1950s, Margolin aspired to become a doctor, yet was always interested in acting and decided to give it a try following insistence from her father's friends.

[2] She attended the High School of Performing Arts and, just prior to her graduation, did a screen test for Five Finger Exercise, where she was urged to sign a contract but declined, instead returning to New York.

[3] Margolin's earliest acting roles were in a commercial for Zest and several instalments in the soap opera The Edge of Night.

[1] In 1961 at the age of 18, while a prop assistant at the New York Shakespeare Festival, Margolin won a pivotal Broadway stage role as Anna in Morris West's Daughter of Silence, beating 200 other applicants.

In 1962, Margolin played her first movie role as the female lead in David and Lisa and traveled to Argentina in 1964 to feature in The Eavesdropper, where upon her return she signed a 1-film-a-year contract with 20th Century Fox.