I have looked at wikipedia. AA were the first ticketing system in "late 50s" with the first real system in 1964. Others may of course know differently.

https://en.wikipedia.org/wiki/Airlin...vations_system

Until the 1950s, airline reservations used manual systems at centralized reservation centers, which consisted of groups of people in a room with physical cards that represented inventory, in this case, seats on airplanes. In the late 1950s, American Airlines wanted a system that would allow real-time access to flight details in all of its offices, and the integration and automation of its booking and ticketing processes. It introduced an electronic reservations system, Magnetronic Reservisor, in 1952.[2] In 1964, it developed the Sabre(Semi-Automated Business Research Environment). Sabre's breakthrough was its ability to keep inventory correct in real time, accessible to agents around the world.[3]

The deregulation of the airline industry, in the Airline Deregulation Act, meant that airlines, which had previously operated under government-set fares ensuring airlines at least broke even, now needed to improve efficiency to compete in a free market. In this deregulated environment, the ARS and its descendants became vital to the travel industry.