Fassi respresented Mexico at the 2014 Summer Youth Olympics and won the Mexican Women's Amateur in 2015, 2016 and 2018. In 2015, she won the Spirit International Amateur in Trinity, Texas, and was runner-up in the South American Women's Amateur. She played college golf at the University of Arkansas where she was 2018 WGCA First-Team All-American, SEC Golfer of the Year and ANNIKA Award winner, in addition to winning the 2019 NCAA Division I Women's Championship individual title and receiving the Honda Sports Award. She received sponsor's exemption to the Walmart NW Arkansas Championship in 2016 and 2018 and in total made six starts on the LPGA Tour as an amateur, including a T15 finish at the 2016 Lorena Ochoa Invitational.
Fassi, who earned her LPGA Tour card in December 2018 deferred membership until she was done with college, and competed as an amateur and turned professional in May 2019, making her professional debut at the 2019 U.S. Women's Open where she finished T12.
Waiting for the 2020 LPGA Tour to resume following the coronavirus pandemic break, Fassi decided to keep her game sharp by entering the Cooper Communities NWA Classic, a Women's All Pro Tour event in Arkansas. She claimed a wire-to-wire, four-shot victory, her first as a professional.
- 2015 Mexican Women's Amateur, Spirit International Amateur
- 2016 Mexican Women's Amateur, Lady Puerto Rico Classic
- 2017 ANNIKA Intercollegiate, Mason Rudolph Women's Championship
- 2018 NCAA Women's South Regional, Darius Rucker Intercollegiate, Lady Puerto Rico Classic, Mexican Women's Amateur
- 2019 SEC Individual Champion, NCAA Women's Division I Individual Champion