Born in Santiago de Cuba, Alcántara's talent for track and field was identified at a young age. She competed in sprinting events and the high jump, but found most success in the triple jump, taking victories at the Cuban schools games in 2002 and 2004. A triple jump/long jump double followed at the 2006 ESPA high school championships. Her international debut came at the age of fifteen at the 2007 World Youth Championships in Athletics. She entered the competition as the world's leading youth athlete with her personal best of 14.21 m and claimed the triple jump title ahead of fellow Cuban Josleidy Ribalta. She also placed seventh in the long jump.