In May 2021, Alvarez was named to the roster of the United States national baseball team for qualifying for baseball at the 2020 Summer Olympics. After the team qualified, Alvarez was named to the Olympics roster on July 2. On July 21, Alvarez was chosen to be a flag bearer for the United States in the Olympics opening ceremony alongside basketball player Sue Bird. Alvarez was the first baseball player to be selected as a flag bearer for the United States. The baseball team went on to win silver, losing to Japan in the gold medal game. Alvarez became the 135th athlete to compete in both the Winter and Summer Olympics and only the sixth to medal at both the Winter and Summer Olympics. Alvarez joined Eddie Eagan and Lauryn Williams as the only three Americans to earn medals at both the Winter and Summer Games.