Álvarez made his professional debut on 31 March 2019, playing the whole 90 minutes in a 4–2 league defeat against Racing Montevideo.[2][3] He scored his first professional goal on 11 May 2019, netting the equalizer in a 1–1 draw against River Plate Montevideo.[4]
Álvarez joined Boston River in April 2021 following Defensor's relegation to Segunda División.[5] On 28 January of the following year, he moved abroad and joined Spanish La Liga side Getafe CF on loan until June 2023.[6]