After two seasons with the Musketeers, Brink entered college a year early,[7] joining the Denver Pioneers for the 2019–20 season.[10] He recorded his first collegiate goal in his Pioneers debut, a 4–3 win over the Alaska Nanooks on October 5.[11][12] During his freshman season, Brink received National Collegiate Hockey Conference (NCHC) Rookie of the Month honors twice: in October, for recording six points in as many games;[13] and in January, when he led all conference rookies with nine points in eight games.[14] Brink missed time at the end of the season with two separate injuries: a strained medial collateral ligament and a cut on his ankle from a skate blade.[4] He finished his rookie season with 11 goals and 24 points in 28 games, and he was unanimously selected to the NCHC All-Rookie Team at forward.[15]
With his freshman season unexpectedly interrupted by the impact of the COVID-19 pandemic on ice hockey and other athletics, Brink spent the 2020 offseason practicing his skating at a local rink.[16] He worked closely with professional figure skater Gathleen Gazich to improve his skating mechanics in preparation for the pandemic-delayed 2020–21 season.[4] That year, Brink was limited to 15 of a possible 24 games due to injury, COVID, and his participation in international tournament.[17] When he did play, he struggled to score, recording only two goals and 11 points on a Pioneers team that failed to qualify for the 2021 NCAA Division I men's ice hockey tournament.[18][19]
The Philadelphia Flyers of the National Hockey League (NHL) selected Brink in the second round, 34th overall, of the 2019 NHL entry draft.[29] On April 10, 2022, the day after winning a national championship with Denver,[28] Brink signed a three-year entry-level contract with the Flyers.[30] He joined the team immediately, making his NHL debut on April 12 against the Washington Capitals.[24] Brink recorded his first professional point in his debut, assisting on James van Riemsdyk's third-period goal during the 9–2 loss.[31] Appearing in 10 games to close out the 2021–22 season, Brink assisted on four goals for the Flyers.[32]
While training in preparation for the 2022–23 season, Brink tore his left acetabular labrum, requiring surgery and sidelining him for the start of the year.[33] He returned to play on January 3 and was assigned to the Lehigh Valley Phantoms, Philadelphia's American Hockey League (AHL) affiliate, to continue his adjustment to professional hockey.[34] It was difficult for Brink to build stamina and return to his pre-injury form during his time with the Phantoms.[35] Coach Ian Laperrière praised Brink's "hockey IQ and the skills that he's got", which allowed him to navigate his subdued physical capabilities.[7] Brink spent the entire season in Lehigh Valley, as the Flyers did not want to disrupt his progress,[35] and finished the regular season with 12 goals and 28 points in 41 AHL games.[36] Brink also appeared in three playoff games with the Phantoms, recording one assist in the process.[36]
Considered unlikely to begin the 2023–24 season in the NHL, Brink impressed the Flyers during the preseason and was named to the opening-night roster.[37] He scored his first two NHL goals on October 26, during Philadelphia's 6–2 win over the Minnesota Wild.[38] After starting the season with six goals and 17 points through 29 games,[39] Brink's quality of play declined by mid-January.[40] On January 22, following a seven-game pointless streak and three healthy scratches in a row, Brink was demoted to Lehigh Valley to continue his development.[41] After 11 games with the Phantoms, during which he posted six goals and 11 points, Brink returned to the Flyers on February 27.[42] After putting up 11 goals and 23 points in 57 games for the Flyers, Brink was sent to Lehigh again on April 17, this time to push the Phantoms towards the 2024 Calder Cup playoffs.[43] He scored in the Phantoms' regular-season finale, a 3–0 victory over the Bridgeport Islanders to clinch a playoff position,[44] and added four assists in six postseason games.[45]
Prior to the 2024–25 season, the Flyers signed Brink to a two-year, $3 million contract extension.[46] Building on his previous season, Brink told reporters that he wanted to increase his confidence and consistency as a two-way player the coming year.[47]
Brink made his international debut with the USA Hockey National Team Development Program at the 2018 World Junior A Challenge.[48] After fracturing his ankle blocking a shot during the semifinal round,[5] Brink scored in the championship, a 2–0 win over Team Russia, to take his team to a gold medal.[49] Brink's eight points were tied for the tournament lead,[48] and he received both MVP and All-Star Team honors.[50] The following year, Brink joined Team USA again for the 2019 IIHF World U18 Championships in Sweden.[51] He recorded three goals and six points in five tournament games, including a goal in Team USA's bronze-medal victory over Team Canada.[46][48]