Born Marguerite Claire Luft in 1926, Piazza grew up in the musical hotbed of New Orleans and seemed destined for stardom. She began publicly performing at the age of two and quickly fell in love with the limelight. "I realized that I wanted to be a singer very early, because practicing the piano and practicing the violin was not appealing to me at all. But when I started to sing? Ah, the world opened up to me. It's what I was born to do," she said. Displaying a true commitment toward honing her craft, Piazza received fine arts degrees from both Loyola University's College of Music and Louisiana State University, where she first discovered her love of opera.
Following graduation, the singer moved to New York City under her mother's maiden name, believing that the Italian name Piazza would give her some added gravitas in the world of opera. In 1944 at the age of 18, Piazza became the youngest member of the New York City Opera, making her debut in the role of Nedda in Leoncavallo's Pagliacci. In subsequent seasons she sang soprano in productions of La Bohème (as Musetta), Don Giovanni (as Donna Elvira), Amelia al Ballo (as Amelia), and The Gypsy Baron. Each performance was met with rave reviews. In 1945, Piazza returned home and made her debut with the New Orleans Opera, starring in the title role of Flotow's "Martha."