Godoy started out with Boca Juniors, before heading to Berazategui in 2015.[3] In 2018, Racing Club signed Godoy; he scored thirty-two goals in his final season with Berazategui's academy.[4][5] Towards the back end of 2020, Godoy moved into first-team football under manager Sebastián Beccacece.[2] He was selected as a substitute for a Copa Libertadores match away to Alianza Lima on 23 September, though wouldn't come on as the club won with two late goals.[2] His senior debut did subsequently arrive on 1 November at home in the Copa de la Liga Profesional against Atlético Tucumán; he was subbed on at half-time of an eventual 4–1 defeat.[2][6][7]