Born in Madrid, Rajado joined the academy of La Liga side Atlético Madrid in 2016, before going on to sign his first professional contract with the club in May 2022, days after turning sixteen.[2] He established himself as a prolific goal-scorer in the Atlético Madrid academy, despite being a winger, and finished the 2022–23 season with twenty-five goals in only twenty-four games.[3][4] The following season, in October 2023, he was named by English newspaper The Guardian as one of the best players born in 2006 worldwide.[5][6]