[1] Failing to attract the attention of any Division I college football programs, Schum committed to play for the Buffalo State Bengals.

Schum continued attending Buffalo State but withdrew from the football team, opting instead to focus on training.

In 2010, under new head coach Jeff Quinn, Schum was granted a tryout at punter and was named the team's starter in each of his final two years of athletic eligibility.

He was selling gym memberships for the Buffalo Athletic Club in the spring of 2013 when he got a call from the Cleveland Browns, who had taken an interest in Schum at an NFL regional combine.

[6] Schum was signed by the New York Jets on June 19, 2014 to compete with incumbent Ryan Quigley in training camp.

[18] In October 2019, Schum was put on the 2020 XFL Draft pool and was selected by the Tampa Bay Vipers in the open rounds.