Veenstra played the role of actual Mormon Battalion member Zemira Palmer in the 2009 production The Mormon Battalion, a film produced by The Church of Jesus Christ of Latter-day Saints to be shown at their San Diego Visitors' Center.
In 2010 Veenstra advanced to the final round of the Irene Ryan Acting competition at the American College Theatre Festival. Later that year, he also won the Best Lead Actor for his role as the lead in Tartuffe from the Theatre and Media Arts department.
After graduation, Veenstra landed the lead role of Hamlet in the Lincoln Center production in New York City. His talent then gave him the lead role of Albert Narracott in the Broadway national tour of War Horse! in 2012.