The biathlon was, in its early form, in the Winter Olympics from the beginning. It was also included in the predecessor to the Winter Olympics, the Nordic Games.
The Nordic Games were founded by Viktor Balck. Balck was an officer in the Swedish army, and his military career was mostly devoted to gymnastics and sports - he was a gymnastics instructor 1870 to 1909, and also the director of the Royal Central Gymnastics Institute for the last three years of that time. He was one of the original members of the International Olympic Committee (IOC). What the (summer) Olympics lacked was snow sports. Balck was the main driver of the development of the Nordic Games, first held in Sweden in 1901, and in Norway in 1903, and then in Sweden in 1905, 1909, 1913, 1917, 1922, and 1926. The goal was partly to have a proto-Winter Olympics, and partly to have a very-Swedish international sporting event.
The Nordic Games included a sport called "military patrol"; this was essentially a team version of the biathlon. The usual team was four, and three of the team would do the target shooting (the "officer" did not). The team wore heavy backpacks during the event in the original version - it was a simulation of a military ski patrol. The backpacks disappeared from competition in later years.
The 1912 Olympics were held in Sweden, and there was discussion of having winter events. However, by this time, the Nordic Games had momentum of their own, and Winter Olympics stayed off the plans in order to protect the Nordic Games. There was further discussion of winter events for the 1916 Olympics, but due to the wartime cancellation of the 1916 Olympics, it didn't happen. The 1920 Olympics included a couple of winter sports: figure skating and ice hockey. The 1924 Olympics (in Paris) brought in the first "official" Winter Olympics, in Chamonix, France. At the time, the official name of these games was "Semaine internationale des sports d'hiver" (International Winter Sports Week), but in 1926, they retroactively became the Winter Olympics: according to the IOC, the new name was the "1st Olympic Winter Games". These 1924 games included military patrol as a sport. Military patrol was dropped as an official medal-winning event, but stayed in the Winter Olympics as a demonstration sport in 1928, 1936 and 1948.
Biathlon entered the Winter Olympics in 1960, not as an entirely new sport - it was a new (non-team) version of the older military patrol. A team version reappeared in 1968, but as a relay rather than the original patrol version.
Postscript: Balck died in 1928, removing one of the great proponents of the Nordic Games. The 1930 games were cancelled due to lack of snow, and then the games themselves were discontinued in favour of the Winter Olympics.