Born in Arocena, Santa Fe Province, Acosta started playing professionally at Unión de Santa Fe, making his top division debut one month shy of his 20th birthday, in a 0–0 home draw against Argentinos Juniors.
It hosted the farewell match for Carlos Valderrama on February 1, 2004, which was attended by players Diego Maradona, Jose Luis Chilavert, Enzo Francescoli, Alberto Acosta, Mauricio Serna, Faustino Asprilla, Arnoldo Iguarán, Leonel Álvarez and the popular singer Carlos Vives.
Alberto Ginastera | Alberto Gonzales | Alberto Giacometti | Alberto Fujimori | Alberto Lattuada | Alberto Salazar | Alberto Burri | Alberto Breccia | Alberto Zaccheroni | Alberto Santos-Dumont | Alberto Magnelli | Alberto Cavalcanti | Alberto Ascari | Nacci Alberto | Alberto Vargas | Alberto Savinio | Alberto Romulo | Alberto Pérez-Gómez | Alberto Bevilacqua | Alberto Acosta | Alberto | Nelson Acosta | José Julián Acosta | Jorge Alberto Rodriguez | Bert Acosta | Alberto Ruiz-Gallardón | Alberto Mancini | Alberto Hurtado University | Alberto Granado | Alberto Cortina |