Starting in 2008, Greene trained in baseball at the Major League Baseball (MLB) Urban Youth Academy in Compton, California. He played on the United States national baseball team in the 2015 18-and-under Baseball World Cup, where the United States won the gold medal. Greene attended Notre Dame High School in Sherman Oaks, Los Angeles, California, where he played for the school's baseball team as a pitcher and shortstop. He finished his high school baseball career with a 1.62 earned run average (ERA) and a .324 batting average, including a 0.75 ERA in his senior year. He participated in the Junior Home Run Derby at the 2016 Major League Baseball All-Star Game, and won.