Buium's professional career began when he signed his entry-level contract with the Minnesota Wild on April 13, 2025, three days after playing for the University of Denver in the NCAA Frozen Four semifinals, when its bid for a second consecutive national championship ended with a 3-2 double-overtime loss to Western Michigan.

The defenseman was a first-round pick (No. 12) by the Wild in the 2024 NHL Draft and had 48 points (13 goals, 35 assists) in 41 games while averaging 27:03 of ice time per game as a sophomore. He was named a finalist for the Hobey Baker Award, a First Team All-American, and selected as the National Collegiate Hockey Conference (NCHC) Player of the Year and the NCHC Offensive Defenseman of the Year.

Buium signed a three-year, entry-level contract with the Wild on April 13, 2025. He had 14 points (three goals, 11 assists) in 31 games as a rookie before he was traded to the Vancouver Canucks in the deal that sent Quinn Hughes to the Minnesota Wild on Dec. 12, 2025.

He had an assist 61 seconds into his Canucks debut, a 2-1 win at the New Jersey Devils on Dec. 14, that made the 20-year-old the youngest defenseman with a point in his first game with Vancouver since Hughes at age 19 on March 28, 2019, which was also his NHL debut. Buium also scored in the first period to make him the third at his position with multiple points at any point during his first game with the Canucks, following Claire Alexander (two goals, two assists, Jan. 28, 1978) and Yannick Tremblay (one goal, two assists, Dec. 8, 2006).

Buium had six points (two goals, four assists) and was plus-10 in seven games to help the United States win the 2025 IIHF World Junior Championship, including an assist on the overtime goal in a 4-3 win against Sweden to secure the gold medal for the second straight year. He had 50 points (11 goals, 39 assists) and 41 blocked shots in 42 games as the second-youngest player in college hockey in 2023-24. He led NCAA defensemen in scoring, ranked third in the NCAA in assists (first among defensemen) and was plus-33 to help Denver win the 2024 national championship with a 2-0 win against Boston College in the title game.