By the late 19th century, the vast grasslands of the Great Plains had been opened up for cattle ranching. This made it possible for many Americans to consume beef almost daily. The hamburger remains as one of the cheapest sources of beef in America.

Adding cheese to hamburgers became popular in 1920. There are several competing claims as to who created the first cheeseburger. Lionel Sternberger is reputed to have introduced the cheeseburger in 1924 at the age of 16. He was working as a fry cook at his father's Pasadena, California sandwich shop, "The Rite Spot", and "experimentally dropped a slab of American cheese on a sizzling hamburger." An early example of the cheeseburger appearing on a menu is a 1928 menu for the Los Angeles restaurant O'Dell's which listed a cheeseburger smothered with chili for 25 cents.

Other restaurants also claim to have invented the cheeseburger. For example, Kaelin's Restaurant in Louisville, Kentucky, said it invented the cheeseburger in 1934. One year later, a trademark for the name "cheeseburger" was awarded to Louis Ballast of the Humpty Dumpty Drive-In in Denver, Colorado. According to Steak 'n Shake archives, the restaurant's founder, Gus Belt, applied for a trademark on the word in the 1930s.

An A&W Restaurants franchise in Lansing, Michigan is credited with inventing the bacon cheeseburger in 1963, putting it on the menu after repeated requests from the same customer.

The steamed cheeseburger, a variation almost exclusively served in central Connecticut, is believed to have been invented at a restaurant called Jack's Lunch in Middletown, Connecticut, in the 1930s.

The largest cheeseburger ever made weighed 2,014 pounds (914 kg). It is said to have included "60 pounds (27 kg) of bacon, 50 pounds (23 kg) of lettuce, 50 pounds (23 kg) of sliced onions, 40 pounds (18 kg) of pickles, and 40 pounds (18 kg) of cheese." This record was set in 2012 by Minnesota's Black Bear Casino, smashing the previous record of 881 pounds (400 kg).

In the United States, National Cheeseburger Day is celebrated annually on September 18.
Given this reference text, how was the cheeseburger invented?
The cheeseburger was invented after the late 19th century after the vast grasslands of the Great Plains opened up for cattle ranching. Once this happened Americans consumed meat daily of which ground beef/hamburger meat was the most affordable.  In 1920, adding cheese to the hamburger meat popular.  It is said that Lionel Sternberger invented the cheeseburger in 1924 while working at his father's sandwich shop.