Garrett began playing basketball at the age of four. He grew up playing basketball, soccer and baseball but mainly focused on football. However, he quit football after breaking his right leg in sixth grade. As a result, Garrett shifted his attention to basketball and began being coached by his uncle and former San Diego State basketball player, Matt Watts. In eighth grade, he joined Watts' Amateur Athletic Union team, Swag House, with whom he competed against high school juniors and seniors. Garrett played for Skyline High School in Dallas and grew from 6'2 as a freshman. In his senior season, he averaged 17.3 points, 10.4 rebounds, 9.1 assists, 3.1 steals and 2.9 blocks per game, leading his team to the Class 6A state semifinals and earning TexasGatorade Player of the Year honors. Garrett was a consensus four-star recruit and one of the top-ranked prospects from Texas in the 2017 class. He chose to play college basketball for Kansas over Texas and Baylor, among others.
College career
In his freshman season at Kansas, Garrett averaged 4.1 points, 3.4 rebounds and 1.1 assists in 19.2 minutes per game. He emerged as a defensive specialist for the Jayhawks but was deemed their "weak link" on the offensive end as he was not a good three-point shooter. On November 13, 2017, he shared Big 12 Conference Newcomer of the Week honors with Mohamed Bamba, after posting 10 points and 10 rebounds in a 92–56 win over Tennessee State. In his sophomore season, Garrett improved as a decision-maker, which helped him earn more playing time. He missed six games in February 2019 with a high ankle sprain. At the end of the season, Garrett was named to the Big 12 All-Defensive Team after averaging 7.3 points, 4.2 rebounds and 1.4 steals per game. As a junior, he averaged 9.2 points, 4.7 assists, 4.5 rebounds and 1.8 steals per game and started in all 31 games. On February 15, 2020, Garrett scored a career-high 24 points with six three-pointers, five rebounds, seven assists and four steals in an 87–70 win over Oklahoma. He was named Big 12 Defensive Player of the Year while also earning All-Defensive and third-team All-Big 12 accolades. On April 1, 2020, Garrett was named the Naismith Defensive Player of the Year Award winner.