Pappas was born in Brooklyn, New York to Greek parents Chris Pappas, an Army officer, and Anna Pappas née Mamalakis, a lawyer originally from Rethymno, Crete. He was raised in the Brooklyn neighborhood of Park Slope with his two older brothers, Peter and Nikos. The former is a lawyer who worked for the Clinton and Obama administrations.

Pappas attended college at the American University in Washington, D.C. where he studied American Studies and History.