Siegel's junior career began in 2019 when he joined the final round of the Formula 4 United States Championship at Circuit of the Americas, competing for Jay Howard Driver Development and finishing in the top ten in both races. He returned to the championship for the opening rounds of the 2020 season with the same outfit.
In the U.S. F2000 National Championship, Siegel first competed full-time in 2019 with Newman Wachs Racing, finishing fifteenth. He returned in 2020 with Jay Howard Driver Development, recording two podiums at Mid-Ohio. For 2021, he joined DEForce Racing, secured his first series win at New Jersey Motorsports Park, and ended the season eighth in the standings.
Siegel made a brief Indy Pro 2000 debut at Gateway Motorsports Park in 2021 with DEForce Racing, finishing fifth. He then moved to the series full-time in 2022 with the same team. At St. Petersburg he took his maiden win in the series, beating Louis Foster on a late restart, and followed it with a dominant flag-to-flag victory at Barber Motorsports Park. Despite the strong early showing, inconsistency in the second half of the season left him fourth in the final standings.
Siegel made his Indy NXT debut at the final round of 2022 at Laguna Seca with HMD Motorsports with Dale Coyne Racing. He returned to the series full-time for 2023 with the same team, winning two races, scoring five podiums total, finishing third in the championship, and claiming the top rookie honor.
For the 2024 season Siegel and HMD reunited for a championship challenge. He took pole and won lights-to-flag at the St. Petersburg opener.
In 2023, Siegel contested the LMP2 class of the Asian Le Mans Series with Inter Europol Competition alongside Charles Crews and Christian Bogle. The team won at Dubai after Siegel passed Charlie Eastwood in the final stint, though two retirements restricted them to fifth in the standings. He also won two LMP2 class races in the IMSA SportsCar Championship that year.
For 2024, Siegel made his debut at the 24 Hours of Le Mans with United Autosports alongside Oliver Jarvis and Bijoy Garg, winning the LMP2 class in his first attempt.
Siegel's IndyCar involvement began with a test for Dale Coyne Racing at Homestead-Miami Speedway in January 2024. He was then announced as a part-time driver in the No. 18 Honda entry for Dale Coyne Racing, sharing the seat with Jack Harvey across four events that did not conflict with his Indy NXT calendar. He attempted to qualify for the 2024 Indianapolis 500 but crashed during his final qualifying attempt and failed to make the field.
In June 2024, he substituted for Agustín Canapino at Road America after Canapino took a leave of absence. Shortly thereafter, Théo Pourchaire was dropped by Arrow McLaren, and Siegel was signed as his permanent replacement. He made his Arrow McLaren debut at the Monterey Grand Prix.
Beyond motorsport, Siegel earned a pilot's license during his time living in Indianapolis, drawn by both convenience for travel to Midwest race events and a personal interest in aviation. He was admitted to Stanford University but deferred enrollment to pursue his professional racing career.