His parents were divorced when Don was two and his mother moved the family to San Pedro, California, a neighborhood located in the Harbor Region of Los Angeles, in 1942.

[5] The aspiring fullback was able to crack the starting lineup during his junior and senior years of high school, however,[6] making his mark as a blocker and ball-carrier on offense while showing the first glimpses of top-level play as a linebacker on the defensive side of the ball.

During his 1952 senior season, Shinnick scored one touchdown in each of San Pedro's seven games, followed by one in the Los Angeles Milk Bowl.

[7] He was named a first-team member of the All-Los Angeles football team as "blocking back"[8] and was Co-Player of the Year in the Eastern Marine League for his efforts.

[9] Under the one-platoon system reinstated in college football in 1953, Shinnick again played fullback on offense and linebacker on defense for the Monarchs, while also handling the team's punting duties.

[10] Although he missed some time with injuries, Shinnick still managed to shine, winning accolades as the best Junior College football player in the Greater Los Angeles area.

[10] On February 15, 1954, Shinnick took his talents to the University of California, Los Angeles (UCLA) when he headed a list of 15 sports stars enrolling at the college.

[15] Barred from participating in the Rose Bowl by the Pacific Coast Conference's "no repeat" rule, undefeated UCLA ended the 1954 season watching their rival USC Trojans lose to Ohio State, resulting in a shared national crown between the Bruins and the Buckeyes.

[16] With "The Bull" trapped on the depth chart behind PCC rushing leader Bob Davenport and second-stringer Doug Peters, regarded as among the best fullbacks in school history,[17] UCLA head coach Red Sanders tried to slide him into the regular rotation with a position switch to guard, with Shinnick to remain on the field on the defense as a linebacker.

[22] In an injury-wracked junior season, Shinnick would play a total of just over 183 minutes of football,[10] with the 9–1 Bruins ultimately losing to Michigan State by a field goal in the Rose Bowl.

[25] In committing to Shinnick, the Colts had to overcome fears that he would follow the example of his friend and UCLA teammate Bob Davenport, who refused to play in the NFL for religious reasons — most of the league's games being held on Sunday, the Christian Sabbath.