Bob Gibson's father, Pack Gibson died from tuberculosis three months prior to Robert Pack "Bob" Gibson's birth. Bob was the youngest of seven children (five boys and two girls). Bob's older brother Josh Gibson, 15 years Bob's elder, served as a mentor and played an influential role in his life and early sports career. Bob Gibson played baseball and basketball in youth leagues, including the YMCA, many of which were coached by Josh. As a 15-year old playing for the YMCA Monarchs in an American Legion baseball tournament in 1951, Gibson and the team coached by Josh, would become the first African American team to win the Nebraska State Championship.

Gibson attended Omaha Technical High School, where during his tenure he participated on the track, basketball, and baseball teams. Health issues resurfaced for Gibson though, and he needed a doctor's permission to compete in high school sports because of a heart murmur that occurred in tandem with a rapid growth spurt. Gibson ran track and field during his first three years because the baseball coach did not want African Americans on the team. When the baseball coach was replaced before Gibson's senior year the path was clear for him to play on the high school's baseball team. Gibson was named to the all-state basketball team as a senior in high school and was awarded a scholarship to attend and play basketball at nearby Creighton University (where his brother Josh earned his college degree). He turned down an opportunity to play for th Kansas City Monarchs of the Negro Leagues. At Creighton, Gibson excelled in basketball, making the Jesuit All-American third team in his junior season. He also played baseball at Creighton, but considered it his second sport.

Gibson graduated from Creighton in 1957 and signed a $3000 contract with the Cardinals, but he was also being persued by the Harlem Globetrotters. The two teams arreanged for Gibson to play the season with the Cardinals farm team, the Columbus (GA) Foxes, then finish the season with the Globetrotters for a total of $8000 between the two organizations. Gibson stopped playing for the Globetrotters when the Cardinals offered him $4000 to focus solely on baseball.