Lee was born Sunisa Phabsomphou^[5]on March 9, 2003 in St. Paul to Yeev Thoj, a healthcare worker.^[6][4] When she was 2 years old her mother met John Lee, who became Sunisa's father. Although her parents never legally married, she made the decision to change her last name to his.^[7] Lee is of Hmong descent;^[8][9] both of her parents immigrated from Laos when they were children.^[7] She has five siblings, sisters Shyenne and Evionn and brothers Jonah, Lucky and Noah.^[6][8] Evionn also competed in artistic gymnastics at the regional level.^[10] She currently lives in St. Paul. ^{[11] [12]}

At six years old,^[6] Lee started gymnastics at the Midwest Gymnastics Center in Little Canada, Minnesota,^[10]a St. Paul suburb, where she still trains. The following year, Lee began competing and won the all-around at a state meet, the second meet of her career.^[8] At age eight, she moved up three levels.^[8] She qualified for elite at eleven years old.^[8]

In August 2019, just days before Lee competed in her first senior US National Championships, her father fell out of a tree while helping a friend, leaving him paralyzed from the waist down.^[13] The following year, Lee's aunt and uncle died from COVID-19. When discussing these tragedies, Lee said, "I am tougher because of it."^[10]