Born in Madrid, Spain, Javier Rivet began his ballet training at La Escuela de Ballet Miriam Sicilia at the age of six. In 2010, he was accepted into the Real Conservatorio Profesional de Danza Mariemma in Madrid, receiving the Premio Extraordinario Fin de Carrera upon his graduation in 2016. In addition, he attended summer programs at English National Ballet, Victor Ullate School, Curso de Danza Menorca and IBStage. During his training, Rivet danced soloist and principal roles in Paquita, La Bayadère, Don Quixote, La fille mal gardée and Raymonda. In 2016, he won first place in the Castellón Dance Competition.
Rivet joined the American Ballet Theatre Studio Company in September 2016 and became an apprentice with the main Company in January 2018.