Quick answer: organised cheerleading is generally traced back to the late 1800s, with November 1898 - when University of Minnesota student Johnny Campbell led the crowd at a football game - most commonly cited as cheerleading's starting point.
The Late 1800s Starting Point
Crowd noise at American college sports existed before any organised role for leading it, but organised group yells were already part of Princeton football by the 1870s and 1880s, and the idea spread to other colleges - including the University of Minnesota, where Johnny Campbell's 1898 crowd chant is the moment most often cited as the start of cheerleading. See Who Invented Cheerleading? for the most commonly cited individual moment within this period.
Early 1900s: Formalisation
Through the early 20th century, yell leading spread to more colleges and became more structured, with recognised squads and, eventually, organised tryouts - though it remained closely tied to supporting football and other college sports rather than existing as its own event.
Mid-1900s: Growth and Change
The University of Minnesota first allowed women to cheer in 1923, and by the mid-20th century - accelerated by the Second World War - cheerleading had shifted from a male-dominated activity to one performed predominantly by women. Lawrence Herkimer founded the National Cheerleaders Association in 1948, spreading cheer camps and standardised technique - see When Did Women Start Cheerleading? for that part of the timeline - while also incorporating more athletic elements like jumps and eventually tumbling.
Late 1900s: Toward Competition
From the 1970s, cheerleading increasingly split into sideline cheer and competitive cheer: the Universal Cheerleaders Association was founded in 1974, a collegiate cheerleading championship was broadcast on CBS in 1978, and All Star gyms grew from the 1980s, leading to the founding of the U.S. All Star Federation in 2003. See When Did Cheer Become a Sport? for more on this shift.
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: Cheerleading (Wikipedia); History of Cheerleading (USA Cheer); Being a Cheerleader - History of Cheerleading (Varsity)