Born in Sabadell, Barcelona, Catalonia, Quesada joined FC Barcelona's youth setup in 2003, aged nine, after starting it out at CE Mercantil. He was released in 2013, and subsequently had trials at Stoke City, Liverpool and PSV Eindhoven; he also signed a four-year deal with Genoa C.F.C. shortly after, but it was declaread void after he failed a medical.
