A youth academy product of Juventud, Falcón made his professional debut on 10 April 2016 in a 0–0 draw against River Plate.[3]
Falcón joined Boston River prior to 2018 season and became club's first-choice goalkeeper.[4] He made his continental debut on 11 April 2018 in a 2–1 loss against Colombian side Jaguares de Córdoba.[5]