 Born in Reus, Tarragona, Catalonia, Cuenca began playing football with local Unió Barri Juroca, going on to have spells with RCD Espanyol, FC Barcelona, UE Barri Santes Creus, CF Reus Deportiu and CF Damm before return to La Masia in 2009.He made his senior debut in the 2010–11 season, being loaned to another club in his native region, CE Sabadell FC in the third division; he made an immediate impact, starting in 24 of his appearances and totalling 2,288 minutes as the "Arlequinats" returned to the second level after an 18-year absence.In July 2011, Cuenca returned to Barcelona and joined its B-team, alongside Martí Riverola.