Belinfante was born into a musical family. Her father, Aron, was a prominent pianist and teacher in Amsterdam who was the first pianist to present the entire cycle of Beethoven piano sonatas during a single season in the Amsterdam Concertgebouw. Belinfante began her study of the cello at age 10. She graduated from the Amsterdam Conservatory and made her professional debut in the "Kleine Zaal" recital hall of the Concertgebouw at age 17, assisted at the piano by her father. Her father died a few months after. Following her debut, Belinfante studied intermittently with cellist Gérard Hekking in Paris, with whom she developed a close friendship.