After being part of the USA Hockey National Team Development Program, he was widely considered as a top prospect for the 2017 NHL entry draft.

[3] After spending his freshman year at Lakeville North High School, Oettinger committed to the USA Hockey National Team Development Program (USNTDP) Juniors for the 2014–15 season.

[12] On September 8, 2020, he made his NHL debut in relief of Anton Khudobin in the third period of the second game of the 2020 Western Conference Final against the Vegas Golden Knights.

He became the starter on arrival, and earned a 30–15–1 record with a .914 save percentage in the regular season, credited as a key factor in the Stars qualifying for the 2022 Stanley Cup playoffs.

[16] However, the series proved far more competitive than expected, a fact that was widely attributed to Oettinger, who was dubbed "bar none, the first star of the first round" by The Hockey News.

[19][18] The Stars were eliminated when Flames forward Johnny Gaudreau finally scored in overtime to end the game 3–2, with Oettinger commenting afterward that he felt he was "just scratching the surface of where I'm going to be one day.