Point played Junior hockey with the Carleton Place Canadians for one year during the 2015–16 season. During that season, he led the Canadians to the Fred Page Cup and was named to the Tournament All-Star Team. Leading up to the 2016 NHL Entry Draft, Point was ranked fourth overall for North American goaltenders by the NHL Central Scouting Bureau. Point was eventually drafted in the 5th round, 128th overall, by the Dallas Stars in the 2016 NHL Entry Draft. Despite having the option to join the Erie Otters in the Ontario Hockey League, Point kept his commitment and attended Colgate University that year on a Division 1 hockey scholarship.
Collegiate
While majoring in Educational Studies at Colgate University, Point played in only 10 games for the Raiders in his freshman season due to an illness. In those 10 games, Point recorded a.918 save percentage. At the end of the season, Point was awarded the Judge Harry J Reynolds Memorial Trophy for his dedication to hockey. Point's sophomore season was much more successful. He played in 33 games and recorded a 16-12-5 record with a.944 save percentage during the 2017–18 season. At the conclusion of the season, Point was named an AHCA East Second-Team All-American as well as a top 10-Hobey Baker Award finalist and NCAA Second All-Star Team. Point was planning on re-joining Colgate University the following season but was convinced by Stars general managerJim Nill and player development coordinator Rich Peverley to turn professional earlier. On July 1, 2018, the Stars signed Point to a three-year, entry-level contract.
Professional
Point began the 2018–19 season in the American Hockey League with the Texas Stars after being cut from the Dallas Stars training camp. After playing five games in the AHL, Point was assigned to the Stars ECHL team, the Idaho Steelheads, where he made his debut on November 7, 2018. On November 18, he was reassigned to the Texas Stars after playing in four games.
International play
Having the choice to play for either the United States or Canada due to being a dual citizen, Point has chosen to represent Canada internationally. He was named to Team Canada's junior team at the 2018 World Junior Ice Hockey Championships where he played backup to goaltender Carter Hart. Point played one game during the tournament, a 6–0 shutout against Slovakia to help Canada on the route to gold.