Schulte was also a three-year varsity starter on the basketball team and helped the Vikings to a fourth-place finish in the Missouri Class 5A state championship.

[5][6] He appeared for Saint Louis FC on May 15, 2019, starting in a Lamar Hunt U.S. Open Cup fixture against Des Moines Menace, helping the team progress in a penalty shootout win.

In 2021, he was again named A-10 first-team All-Conference, as well as United Soccer Coaches second-team All-Region, and Most Outstanding Player of the A-10 Championship.

[11][12] On January 6, 2022, it was announced that Schulte would leave college early and sign a Generation Adidas contract with Major League Soccer, allowing him to enter the 2022 MLS SuperDraft.

[20][7] Schulte made his debut for the senior United States national team on January 20, 2024, in a friendly against Slovenia.