Born in Santa Brígida, Las Palmas, Canary Islands, Curbelo finished his formation with UD Telde,[3] making his senior debut during the 2013–14 season, in Tercera División.
On 20 August 2015, he signed a contract with Segunda División B side SD Leioa,[4] but terminated his link in December after being rarely used.
[5] On 28 December 2015, Curbelo joined UD Las Palmas, club he already represented as a youth, and was assigned to the reserves in the fourth division.
[7] Curbelo made his professional debut on 7 January 2019, starting as a right back in a 0–0 away draw against CF Rayo Majadahonda.
[11] On 10 July 2024, free agent Curbelo signed a two-year deal with Sporting de Gijón in division two.