Custer began racing quarter midgets at age four. In 2011, Custer won the USAC National Focus Young Guns Championship. The following year, Custer began racing late models, winning ten races and earning Rookie of the Year honors.
In 2014, Custer joined Haas Racing Development to run nine races in the NASCAR Camping World Truck Series, making his debut in the Kroger 250 at Martinsville Speedway. Custer started the race 9th, and finished 12th. In qualifying for the Drivin' for Linemen 200 at Gateway Motorsports Park, Custer set the track record with a lap speed, becoming the youngest pole winner in NASCAR history. At New Hampshire Motor Speedway on September 20, 2014, Custer won the Camping World Truck Series' UNOH 175 from the pole, becoming the youngest winner in the history of NASCAR's national touring series at 16 years, 7 months and 28 days. On January 12, 2015, JR Motorsports announced that Custer would drive a truck for them in ten races in 2015. On June 13, Custer won the Truck race at Gateway Motorsports Park, holding off the No. 23 truck of Spencer Gallagher, after the dominating trucks of Erik Jones and Matt Crafton were involved in two wrecks at laps 142 and 152. When he turned 18 years old in 2016, JR Motorsports began fielding the No. 00 truck for Custer full-time, competing for the Rookie of the Year title. At Canadian Tire Motorsport Park during the Chevrolet Silverado 250, John Hunter Nemechek and Custer were battling for the lead when Nemechek bumped Custer before running both Custer and himself off-road, pinning Custer to the wall. Before the winner was declared, Nemechek was tackled by Custer; Nemechek would be named the winner.
In 2016, Custer made his Xfinity Series debut for JR Motorsports at Richmond International Raceway, driving the No. 5 Chevrolet Camaro. He drove the No. 88 for JR Motorsports to a career best fourth-place finish at Charlotte in the Hisense 4K TV 300. On September 16, 2016, Stewart-Haas Racing announced that Custer would drive the No. 00 Ford Mustang full-time in 2017, with Haas Automation as the primary sponsor. Custer began the 2017 Xfinity season with a crash at Daytona, finishing 37th. He rebounded the next week at Atlanta, finishing 10th. After making the Playoffs in his first appearance, Custer began making a surge at the end of the season including leading the most laps at Chicago and Kansas. Custer missed the Final Four by two spots after racing head to head with Daniel Hemric, the next week, Custer put on a clinic by leading the most laps, winning both stages and en route to his first Xfinity win at the Homestead–Miami Speedway in South Florida. The next year at the fall Texas race, Custer got his second career win when he passed Tyler Reddick on the last lap, clinching his spot in the Championship Four. In the 2019 season, Custer scored wins at Fontana, Richmond, Pocono, Chicago, Kentucky, and Dover. He finished second at Darlington, but was declared the official race winner after Denny Hamlin was disqualified when his car failed to meet height requirements during post-race inspection. At the end of the Kansas race, Custer got into a fight with Reddick on pit road. Custer finished the 2019 season second in points after finishing second again to Reddick at Homestead.
