Quick answer: there's no single date cheer "became a sport" - it shifted gradually from the mid-20th century onward as judged competitions developed, and this shift is still ongoing today through official sport recognition processes with bodies like the International Olympic Committee.
A Gradual Shift, Not a Single Moment
Unlike sports with a clear founding date, cheerleading's transition from sideline crowd support into a competitive sport happened gradually, as more skill-based elements (jumps, tumbling, stunts) were added and organisations began running events that judged squads directly against each other. See How Did Competitive Cheer Develop? for that fuller story.
Televised Competition Raised the Profile
A collegiate cheerleading championship was broadcast on CBS in 1978, and ESPN began broadcasting UCA's championships in the early 1980s. Televised competition presented cheer to a national audience as a skill-judged activity in its own right rather than an accompaniment to another sport.
Formal Sport Recognition Is a Separate, Ongoing Process
Being widely understood as a competitive sport is different from formal recognition by major sporting institutions. Competitive cheer's governing bodies have pursued official recognition as a distinct, later process from the sport's grassroots growth. The International Cheer Union, founded in 2004, received provisional recognition from the International Olympic Committee in December 2016 and full recognition in July 2021. See Cheerleading and Olympic Recognition for where that stands.
Where Things Stand Today
Competitive cheer is treated as a sport by governing bodies, competition providers and, since 2021, by the International Olympic Committee - although recognition by individual schools, colleges and national sports bodies still varies from place to place.
A Note on Dates
Some early details vary slightly between sources. Where sources disagree, we give the most widely cited version and avoid false precision - the sources we used are listed below.
Sources: UCA Division I-A College National Championship (Wikipedia); About the ICU (International Cheer Union); IOC's Full Recognition Marks Another Milestone for Our Sport (ICU Europe)