Stroud graduated from Hazel Green High School in 2006. He earned his bachelor of arts in history and political science at UAB in 2010. He performed as first trumpet in the UAB Wind Symphony and as president of the UAB Student Government Association and student representative to the University of Alabama Board of Trustees. He went on to complete a master's in urban education and public policy at the University of Pennsylvania in 2012, working as a civics teacher with "Teach for America" at the Boys' Latin of Philadelphia Charter School. Stroud completed his juris doctorate at the Washington & Lee University School of Law in 2015. He served as managing editor of the Washington & Lee Journal of Civil Rights & Social Justice and was a finalist in the 2014 John W. Davis Moot Court Competition.
The next year, Stroud served as a Visiting Academic Fellow at Yale Law School's Information Society Project and was also made acting director of development and policy for the New Haven, Connecticut mayor's office. In 2016 he clerked for Judge Madeline Haikala at the U.S. District Court for the Northern District of Alabama. In 2017 he was tapped as a visiting assistant professor at Washington & Lee. He began his present clerkship in 2018.