Gee in played baseball at Cleburne High School in Cleburne. In his first start in his senior year, Gee pitched a no-hitter, falling one out short of a perfect game. He later threw a second no-hitter, finishing the year as the team's Most Valuable Player and earning first team all-state and all-district honors. As a batter, he hit .443 with six home runs and 46 RBI in his senior year. He also played for the school's golf team.
In 2005, Gee attended the University of Texas at Arlington and played baseball for the Mavericks. At UT Arlington, Gee helped the Mavericks to a berth in the 2006 NCAA tournament. He ranks second on the school's career list with 298.1 innings pitched and was a two-time honorable mention All-Southland Conference recipient (2005 and 2006).
Gee was drafted by the New York Mets in the 21st round of the Major League Baseball draft and began his professional career with the Class-A Brooklyn Cyclones of the New York–Penn League. He initially worked mostly out of the bullpen yet by season's end, Gee was starting and amassed a 3-1 record with a 2.28 ERA as a starter. In 2008, Gee had a break out year with the Class-A St. Lucie Mets of the Florida State League (FSL), winning the Sterling Award and being named to the FSL All-Star team. Later in 2008, Gee was promoted to the Class-AA Binghamton Mets of the Eastern League where he went 2-0 with a 1.33 ERA in 4 games. In 2009, Gee started the season with the Class-AAA Buffalo Bisons of the International League yet was shut down May 25 due to a torn labrum in his right shoulder.
In 2010, Gee had a bounce back season and recouped his health after his season-ending injury in 2009. He went 13-8 for Buffalo, and led Class-AAA with 165 strikeouts in 1611⁄3 innings, yet he gave up more than a hit per inning and finished with a 4.96 ERA. Nonetheless, Gee made his major league debut with the Mets on September 7, marking the first time in Mets history that two starting pitchers made their major league debuts in the same game, as Gee faced rookie Yunesky Maya of the Washington Nationals. Gee also became the first Mets pitcher to record an RBI in his major league debut. He pitched brilliantly in his debut, taking a no-hit bid into the 6th inning when Willie Harris broke it up with a lead off home run. He finished giving up only two hits and one run in seven innings. Gee stayed with Mets until the end of the season, compiling a 2-2 record with a 2.18 ERA in 5 starts.