Begay is a lifetime resident of Arizona and grew up on the Navajo Nation near Black Mesa and was raised under the teachings of his ancestry, instilling in him the importance of remembering the story of his people and carrying it on to his descendants.

[citation needed] Begay graduated from the University of Arizona with a Bachelor of Science degree in Molecular and Cellular Biology and was a student in the Minority Medical Education Program at the University of Arizona College of Medicine.

He also attended the Arizona International College's Natural Sciences and Mathematics program in Tucson, Arizona; Johns Hopkins Bloomberg School of Public Health's Winter Institute, in Baltimore, Maryland; and the Harvard School of Public Health's Public Health Studies program in Boston, Massachusetts.

[4] He served as the co-chair of the Native Americans for Trump 2020 coalition, together with fellow Navajo Sharon Clahchischilliage.

He enjoys spending time with his nephew Matthew, who frequently visits from Tucson.