Burcham was born in Phoenix, Arizona, but has lived in La Quinta, California for most of his life.[3][4] His parents are Tim and Mimi Burcham, and he is Jewish.[4][5][6][7] His father was drafted by the California Angels in 1985 and played 10 years in the minor leagues for the Angels and San Francisco Giants organizations.[7]
In his junior year in 2014, he batted .300/.351/.367 and ranked fourth in the WAC with 71 hits, ninth with 14 doubles, was fifth in the WAC with 154 assists, and was voted to the All-San Luis Obispo NCAA Regional Team.[4][13] By the end of his junior year he was third in school history with 22 career sacrifice hits.[4] He was voted to the 2015 Preseason All-WAC Team, and in his senior season he batted .329./.382/.465 and had 46 runs (6th in the WAC), 6 triples (leading the conference), 16 stolen bases (4th), and 5 sacrifice flies (leading the conference).[14][10][15]
In the 2017 season he played for the Lancaster JetHawks of the Class A-Advanced California League. Burcham batted .251/.301/.349 over 235 at bats with three home runs, 26 RBIs, and nine steals.[18][19]
In the 2018 season Burcham played for the Hartford Yard Goats of the Class AA Eastern League. He batted .263/.328/.349 over 175 at bats with two home runs, 15 RBIs, and six steals.[20] In 2019 with the Yard Goats he batted .200/.287/.295 over 220 at bats with three home runs, 21 RBIs, and five steals.[20]
Burcham did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[21] He began the 2021 season playing for the Triple-A Albuquerque Isotopes, in his AAA debut.[22] Burcham batted .234/.273/.315 over 124 at bats with 1 home run and 9 RBIs in 52 games played.[20] He missed nearly a month of action during the season in order to play for Team Israel at the 2020 Summer Olympics. Burcham elected free agency following the season on November 7, 2021.[23]
On April 28, 2022, Burcham was traded to the Charleston Dirty Birds of the Atlantic League in exchange for a player to be named later.[25] In 104 games for Charleston, he batted .246/.301/.335 with six home runs, 39 RBI, and eight stolen bases. Burcham became a free agent following the season.
Team Israel
Burcham played shortstop for Israel at the 2017 World Baseball Classic qualifier.[26] Burcham was the starting shortstop in all three games, while batting eighth. During the opening game of the qualifier Burcham went 1-for-4 with a run scored.[27] Burcham went 1-for-3 during the second game; however, he was thrown out on a caught stealing.[28] In the final game, Burcham went 3-for-4, with a strikeout and two runs scored, finishing the series batting .455.[29]
He was the starting shortstop for Team Israel at the 2017 World Baseball Classic in the main tournament, in March 2017.[30] In the tournament's opener, Burcham singled in the game-winning run in the 10th inning in a 2-1 win over South Korea.[9] In the WBC, he batted .261 with two RBIs and a 1.000 fielding percentage.[18]