Esquivel joined the youth categories of Atlético Madrid in July 2021, and signed a professional deal until 2024 in October. After being mainly a member of the Juvenil team, he had a tachycardia episode during a UEFA Europa League match against Celtic on 7 November 2023; he underwent several examinations after the match, and was declared fit to play afterwards, returning to trainings ten days later.
In May 2024, Esquivel suffered a knee injury which sidelined him for most of the season. He still renewed his link until 2027 on 18 July, and made his senior debut with the reserves on 22 March 2025, starting in a 0–0 Primera Federación home draw against Betis Deportivo.
Esquivel then profitted from the departures of both Alejandro Iturbe and Antonio Gomis from the B-team to establish himself as an undisputed starter for the side, while also acting as a third-choice in the first team. On 1 September 2026, he was definitely promoted to the main squad of Atleti, being assigned the number 25 jersey.