She won the B-final of the 400-meter individual medley in Wave I of the 2020 USA Swimming Olympic Trials where she was the youngest swimmer to compete at 13 years of age.

[8][9] On the first day of competition, 28 May, Han broke the 400-meter freestyle national age group record set by Claire Tuggle with a time of 4:17.65.

[9] Han was the youngest swimmer to qualify for the 2020 USA Swimming Olympic Trials, held in Omaha, Nebraska, and postponed to June 2021 due to the COVID-19 pandemic, at 12 years of age.

[19] Her performances leading up to and at the 2020 Olympic Trials were noted by Swimming World who, in July 2021, gave her their "Up & Comers" age group swimmer of the month honor for her achievements.

[20] At the 2021 West Speedo Summer Championships in Irvine, California, in August, Han set personal best times in a number of events including the 400-meter freestyle where she swam a 4:14.52 and ranked as the third fastest female American 13 years of age to swim the race in history.

[22] The following morning, on day two of competition, Han swam a personal best time of 2:03.23 in the 200-meter freestyle prelims and advanced to the championship final of the event ranked fifth overall.

[22][25] For the 2021 U.S. Open Championships, Han entered to compete in six individual events in the pre-scratch stage of lead-up to the start of competition on December 1.

[29] In the fastest final heat, called the a-final, of the 400-meter individual medley on the third day of competition, Han placed fourth with a personal best time of 4:47.92 in the event, finishing less than 10 seconds behind the gold medalist Leah Smith.

[36] In April, she swam best times in the 400-meter individual medley, a 4:46.01 that ranked as the fastest all-time for 13-year-old American girls, and the 200-meter freestyle, a 2:02.17, at the 2022 Fran Crippen Swim Meet of Champions.

[39] In the 800-meter freestyle on the first day of the 2022 US International Team Trials in Greensboro, North Carolina, in late April, Han placed fifth in the slowest heats with a personal best time of 8:41.02.

[46][47] She was one of four female swimmers named to the roster in individual medley events along with Teagan O'Dell, Julia Podkościelny, and Emily Thompson.

[47] On the first day of competition at Veterans Memorial Aquatic Center in Honolulu, she achieved a personal best time of 8:35.85 in the 800-meter freestyle and ranked ninth overall when the results from the slowest and fastest heats were merged.

[48][49] In the evening, she finished in a personal best time of 4:43.60 behind Mio Narita of Japan to win the silver medal at 14 years, 86 days of age.