Sarmiento joined Estudiantes in 2009, after spells with Defensores de Bosques and Independiente.[4][5] He made his debut in senior football at the age of sixteen, after manager Gabriel Milito promoted him into Estudiantes' first-team squad during the 2019–20 campaign.[6][7] After going unused on the substitute's bench for Primera División fixtures with Patronato and Arsenal de Sarandí in September, Sarmiento's bow arrived on 5 October 2019 in a goalless draw at home to Huracán; replacing Diego García after sixty-seven minutes to become the club's second youngest debutant.[8][9][10][11] Seven more appearances came in his breakthrough season.[2]
On 31 December 2020, Estudiantes vice president Martín Gorostegui confirmed that transfer negotiations were underway with Premier League club Manchester City for Sarmiento; two days after the player had renewed his contract through to 31 December 2021.[12][13][14]
Manchester City
On 30 April 2021, Estudiantes announced that Sarmiento would join Manchester City on 1 July,[15] for a reported initial fee of £5.2million.[16]
Sarmiento regularly featured for the Argentina U16s, including at the Montaigu Tournament and Torneo de Desarrollo; winning both competitions.[18][19][20][21] He also appeared for the U17s under Pablo Aimar.[10][22][23] In December 2020, Sarmiento received a call-up from the U20s.[24]