Galván is youth product of River Plate, having joined their academy at the age of 6. In 2021, he signed a contract keeping him at the club until 31 December 2022. He debuted for River Plate in a Argentine Primera División match against their rivals Boca Juniors in the Superclásico. The game was 1–1 before heading to overtime, and finished 4–2 in penalties.
