Stainbrook is the son of Dave Stainbrook who was a standout 6'7" football player at Ohio University in the early 1980s and also a software engineer in the aerospace industry who once worked for NASA, grew up in suburban Cleveland. In a 2015 interview with New York Times reporter John Branch, he admitted to having been a "nobody" in high school; he did not start for his high school varsity team until his senior year. He initially planned to play at local Division III school Case Western Reserve University until receiving a Division I offer from Western Michigan University.
College career
Despite being almost completely ignored out of high school, he earned the starting center position as a freshman at Western Michigan. Notably, his first game was against Xavier, and he had 10 points and 7 rebounds in what proved to be a difficult 68–65 win for Xavier. According to Branch, Musketeers coach Chris Mack "wondered how the center—with his crazy hair, pads on his knees and elbows, and goggles on his face—had gone unnoticed in recruiting." Ultimately, Stainbrook would transfer to Xavier after his sophomore season. Mack had some conditions before accepting him—he would have to cut his hair, stop wearing knee and elbow pads and lose 50 pounds. Mack also wanted to remove Stainbrook's goggles, but relented when Stainbrook told him they were prescription goggles that he needed in order to see well enough to play. He went on to earn second-team All-Big East honors in his final college season of 2014–15, and was also one of the 10 finalists for that season's Senior CLASS Award. He averaged just under 12 points and 7 rebounds per game in leading Xavier to the Sweet 16. Following the season Stainbrook joined the Xavier track and field team as a discus thrower and shot putter, and competed at the Big EastTrack & Field Outdoor Championship at Villanova University.
Stainbrook is the son of Nancy and Dave Stainbrook, and has two brothers. His father, Dave, played football for Ohio University from 1980 to 1985. His older brother Andy is 6'9" and briefly attended the United States Air Force Academy, and younger brother Tim is 6'6", attends Xavier, and played a major role in an episode that brought Matt a significant amount of national notoriety.
During his senior season in 2014–15, Stainbrook not only made news for his on-court play, but also for his part-time job as a driver for Uber. His journey to that job began the previous season when Tim walked on to the Xavier basketball team at Matt's suggestion. Matt completed a bachelor's degree in finance in May 2014 but still had a year of athletic eligibility remaining, and enrolled in the school's MBA program. Tim's undergraduate tuition was about $43,000 per year, while Matt's graduate tuition was roughly $14,000. Even though Tim was receiving a partial academic scholarship, the family would have paid considerably more in education expenses if Matt were on scholarship while Tim was a walk-on. This led Matt to go to Xavier's director of basketball operations and NCAA compliance director and give up his scholarship for his brother. Because he was now a walk-on, he was no longer bound by many restrictions that the NCAA places on student-athletes, most significantly those dealing with off-campus employment. In addition, he had wanted to live off campus, especially in his final season, but Xavier athletic department policy generally requires scholarship athletes to live in university housing; being a walk-on enabled him to fulfill this desire. While student loans paid for most of his direct academic expenses, he still had many other expenses to meet, and a schedule that made most normal jobs impractical. Having used Uber himself while at Xavier, he researched the requirements for becoming a driver for the company. He met all the requirements, with his 2004 Buick Rendezvous barely meeting the 10-year cutoff for eligible vehicles, and was accepted as a driver. During the basketball offseason, he drove for Uber anywhere from 25 to 30 hours per week, dropping his hours to 10 to 20 per week during basketball season. According to Stainbrook, "It sort of relaxes you. You get to talk to people who don’t always want to talk basketball all the time, so it’s a change of pace." He mainly drove in the area of the Xavier campus, and he estimated that about half the people he picked up recognized him, at least by his face and size.