Souza attended Cascade High School in Everett, Washington. In high school, Souza starred for the school's baseball and football teams. Souza committed to attend Washington State University on a baseball scholarship, while also playing football for the Washington State Cougars.

The Washington Nationals selected Souza in the third round of the 2007 Major League Baseball Draft. Souza signed with the Nationals rather than attend college, receiving a $346,000 signing bonus. He played for the Hagerstown Suns of the Class A South Atlantic League in 2009 and 2010. In 2009, he had 116 strikeouts in 126 games. He was selected for the South Atlantic League All-Star Game in 2010, but he also received a 50-game suspension for use of a banned substance.

Souza played for the Potomac Nationals of the Class A-Advanced Carolina League in 2011. Late in the season, he was benched for breaking team rules, and considered leaving the Nationals' organization to play college football. He returned to the Nationals' organization in 2012, and batted .297 with 23 home runs between Hagerstown and Potomac. In 2013, Souza played for the Harrisburg Senators of the Class AA Eastern League, where he batted .300 with 15 home runs and 20 stolen bases in 77 games. He played in the Arizona Fall League after the regular season. He was added to the Washington 40 man roster on November 1, 2013.

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