Schwartzstein is Jewish, and his hometown is Southlake, Texas. His father formerly owned a tire dealership. He attended Carroll High School. As a junior playing left tackle, he helped the Carroll Dragons to 16–0 record and the Texas Class 5A state title, and as a senior he helped the team to an 11–2 record. He was Associated Presssecond team All-State and first team All-District as a senior in 2007. He was ranked the # 52 offensive guard nationally by Scout.com. He was named All-Midwest Region for the Class of 2008 by PrepStar. Schwartzstein had at least eight scholarship offers upon graduating high school, including Stanford, Purdue, and Colorado State. Scout.com's Texas analyst wrote that he:
uses position and leverage to make the plays on the field.... he is quick on the attack, and gets his hands inside the defender; he has enough pop in his hands and arms to not only control the defender but at times to knock him down... he gets the initial contact and the ability to control the situation. Second, he is aggressive in nature and will follow the defender downfield and look for a second block up field... He has good footwork... He is a highly developed tackle prospect... Overall, he is a very good offensive line prospect who plays smart, intelligent football.
He chose to attend Stanford, arriving as a guard. In 2010, he played in his junior year at Stanford in six games as a reserve on the offensive line. In 2011, his senior year, he started all 13 games at center. After his first start, his head coach, David Shaw, said "I think Sammy Schwartzstein was outstanding, was off the charts. We expected him to play well, he surpassed our expectations". He helped Andrew Luck lead the Pac-12in passing efficiency and completion percentage while breaking school records for career and single-season touchdown passes. Stanford also was tied for seventh nationally in fewest sacks allowed per game. He helped running backStepfan Taylor run for 1,330 yards, the second-highest single-season mark in school history. He helped Stanford compile a single-game school record 446 yards rushing in a 65–21 rout of No. 22 Washington. In 2012, as a fifth-year senior considered a team motivator, he was elected a team captain by his teammates, and nicknamed "Coach Sammy" by them. Coach Shaw said "His ability to decipher things at the line of scrimmage and make sure everybody's on the same page is phenomenal. He sees as well as any center I've been around." He was also a preseason candidate for the Rimington Trophy as the nation's top center. Before the 2012 season, Walter Football called him a "sleeper center prospect who deserves more attention." He was quoted in the New York Times as saying "I come from a high school where we ran the spread offense and it was just deep ball, deep ball, deep ball — that’s boring to me.... This is real football, grindstone. That’s how it’s supposed to be played.” In 2012, the Cardinal played 14 games and allowed only 20 sacks. He was second-team All-Pac-12, and received Stanford's athletics plus leadership award, the Al Masters Award.
Some mock drafts had him being selected in the sixth or seventh round of the 2013 NFL draft. His time in the 40-yard dash was 5.12, 7th-best among draft-eligible centers.
