Alvarado made his professional debut on 25 September 2013 in the Apertura 2013 Copa MX group stage match against Estudiantes Tecos, coming on as a substitute for Guillermo Clemens on the 59th minute in a 1–0 win.

[5] Three days later, he made his league debut, also against Estudiantes Tecos, in a 0–0 draw, coming on as a substitute for René García on the 86th minute.

[6] Alvarado scored his first professional goal in the 27th minute of a 1–0 win in a Clausura 2014 Copa MX group stage match against Atlas on 18 February 2014.

[6] It was not until the Apertura 2016 season that Alvarado truly broke out, scoring six goals in 14 games, and catching the attention of Mexican top-flight teams.

[15] Alvarado participated at the 2020 CONCACAF Olympic Qualifying Championship, appearing in all five matches, where Mexico won the competition.

On 29 August 2018, Alvarado received his first call-up to the senior national team for the friendly matches against Uruguay and the United States.

[35] In October 2022, Alvarado was named in Mexico's preliminary 31-man squad for the 2022 FIFA World Cup, and in November, he was ultimately included in the final 26-man roster.

[36] A gifted playmaker whose versatility is his strongest suit, Alvarado is predominantly a central attacking midfielder, capable of playing on either flank as well as a second striker.

The change of pace is Alvarado's favoured technique, and he excels when there's space behind an opponent to race into, but he can also deceive defenders with close control and, at times, thrilling skill.

[38] He is excellent at pulling away from defenders to make himself available for a pass and has a remarkable ability to accurately place floated crosses and through balls.