Sokoli's father, Gjon, fled from Shkodër, Albania[4] to the United States seeking political asylum around the time of the Albanian Rebellion of 1997 when Kristjan was five years old.

Sokoli, known as "Moose" by his high school coach,[5] was a three-year letterwinner in football at Bloomfield High School in Bloomfield, New Jersey where he played defensive end, left tackle, tight end, punter and placekicker.

He suffered fractures on his wrist before junior and senior year of high school, which set him back a bit.

[6] He signed a National Letter of Intent to play at the University at Buffalo in early February of his senior year.

By his junior year, he had become a starter on the line and was an integral part of a Buffalo pass rush which was led by future first-round draft pick linebacker Khalil Mack.

He majored in Business Administration and said that he would like to work on the New York Stock Exchange if he could not make a living playing football.

[13] On September 26, 2016, Sokoli was signed to the practice squad of the Indianapolis Colts as a defensive end.

[25] On March 10, 2022, Sokoli was drafted by the Houston Gamblers of the United States Football League.

[27] On January 8, 2025, Sokoli signed with the Houston Roughnecks of the United Football League (UFL).