Cortés was born in Surgidero de Batabanó, Cuba. His father won the visa lottery when he was seven months old, and they relocated to the United States in the city of Hialeah, Florida.
His father, Nestor Cortés Sr., was sentenced to one year in prison after a failed attempt to defect from Cuba in 1992. Nestor Sr. met his wife, Yuslaidy, the following year.
Cortés started playing baseball at the age of four.[2] His father took him to see the Florida Marlins of Major League Baseball play at Pro Player Stadium in Miami Gardens.