[3][4] Partway through 2022, he started training with Lakeside Aquatic Club, based in Lewisville, Texas, competing for the team at the 2022 Winter Junior US National Championships in December.

[3][4] Later in the year, as a 15-year-old at the 2021 Speedo Winter Junior National Championships in December in Austin, Texas, he won the 200 yard individual medley with a personal best time of 1:43.16.

[9] The following day of competition, he finished in a personal best time of 3:42.22 in the 400 yard individual medley to win the event and rank as the second-fastest male American swimmer in history in the 15-16 age group by 0.14 seconds.

[12] In April, at the 2022 USA Swimming International Team Trials in Greensboro, North Carolina, Williamson placed eighth in the C-final of the 200 meter freestyle on the second day of competition with a 1:54.94.

[21][22][23] In his first final on day two, the 400 meter individual medley, he won the silver medal with a personal best time of 4:17.58, which was 2.35 seconds slower than gold medalist Ei Kamikawabata of Japan.

[5] For his final event, the 200 meter individual medley, he won the gold medal with a Championships record and personal best time of 1:59.01, which lowered the mark 0.50 seconds from the 1:59.51 it was set at in 2012 by Chase Kalisz.

[8] He won three events for his locality, the West edition, the next day, including the 400 yard individual medley with a boys 15-16 National Age Group record of 3:39.83 that was over two full seconds faster than the former record set approximately 20 years earlier, the 200-yard freestyle with a 1:33.60, and the 100 yard backstroke with a personal best time of 46.90 seconds.