Alemán was born in Machagai, Chaco Province, in northern Argentina. He was the fourth child of seven born to pianist Marcela Pereira, a native Argentine, and Jorge Alemán Morales, of Uruguayan descent, who played guitar in a folk quartet with his children Carlos, Juan, and Jorgelina.
At the age of six, Alemán joined the family ensemble, the Moreira Sextet, and played the cavaquinho, a chordophone related to the ukulele, before taking up the guitar. The group travelled to Buenos Aires to perform at the Parque Japonés, Nuevo Theater, and at the Luna Park. Later they toured in Brazil.