Born in New York City, Troyanos spent her earliest days in the Manhattan neighborhood where Lincoln Center, the new home of the Metropolitan Opera, would arise a quarter century later. She grew up in Forest Hills, Queens, and attended Forest Hills High School. Her early childhood was clouded by a deep sense of abandonment; her parents, operatic hopefuls who, she said, "had beautiful voices"—her father, born on the Greek island of Cephalonia, was a tenor, and her mother, from Stuttgart, was a coloratura soprano — had separated when she was an infant and later divorced, "ill-matched to each other and ill-suited to parenthood" (Opera News).
She was looked after by Greek relatives and lived for around a decade at the Brooklyn Home for Children, which had relocated to Forest Hills. She said of her childhood, "My past is hard to overcome." She described the children's home itself as
"bleak but marvelous". It was there that her life in music began. She studied piano for seven years, first at the home, where her instructor was veteran Metropolitan Opera bassoonist Louis Pietrini, who had volunteered to teach the children a variety of instruments — initially teaching them solfège, which Troyanos later called "the basis of my musical education"
— and her studies continued, on scholarship, at the Brooklyn Music School. In several interviews she recalled early expectations of becoming a concert pianist. "Determined since childhood," by other accounts, "to become an opera singer," he sang in school choirs and New York's All City High School Chorus; when she was sixteen, a teacher heard her voice in the chorus and took time "to find out who the voice belonged to ... and got me to the Juilliard Preparatory School and my first voice teacher."
In her late teens, Troyanos moved to the Girls' Service League in Manhattan and later to a co-ed boarding house on E. 39th St., not far from the old Met, which she frequently attended as a standee. She was employed as a secretary to the director of publicity at Random House, and performed in choruses, ranging from church choirs (with a scholarship at the First Presbyterian Church) to musical theater; "Tatiana Troyanos, almost hidden in the chorus, came soaring through with a pellucid and magnificent quality of tone as the Arab Singing Girl," proclaimed the Boston Globe's Kevin Kelly in a review of a summer stock production of Fanny in September 1958.
Continuing at the Juilliard School, Troyanos was chosen as a soloist for Bach's St. John Passion in 1959 and for the Verdi Requiem in 1962, by which time she had begun vocal studies with Hans Heinz, who "understood my voice and helped me open it up at the top ... and gradually I found all my top notes." She described Heinz, with whom she continued to study after her graduation in 1963, as "the major influence in my life ... Our work together built the foundation that was so essential to my career."