The Mexican signed a five-year contract with Ajax in July 2019. Just a month later, on 17 August 2019 to be precise, he made his debut in the away game against VVV Venlo: 4-1. Despite being one of his first ever games, the South American scored almost instantly while wearing the red and white strip. In the UEFA Champions League qualifier against APOEL Nicosia, he made it 1-0. Ajax eventually qualified for the group stage of the European club tournament thanks to a 2-0 victory. In the opening game of that European season, he scored against OSC Lille. Which has been his only goal so far in the Champions League.
Of the hundred matches he has played so far, he has appeared in the Eredivisie 64 times for the Ajax first team. He has scored four times playing there: against ADO Den Haag, Vitesse, FC Groningen and FC Utrecht.
In autumn 2021, he signed a new contract in the Johan Cruijff ArenA at a supporters' event. He has signed a commitment until mid-2025.
Álvarez is the first Mexican on the Ajax squad to have made the 100 Club.