In 2000 (I still cannot find an exact date), Roy Fiedling submitted his dissertation Architectural Styles and the Design of Network-based Software Architectures. It is available at https://www.ics.uci.edu/~fielding/pubs/dissertation/fielding_dissertation.pdf.
In 2006, Amazon Web Services (AWS) began offering IT infrastructure services to businesses in the form of web services -- now commonly known as cloud computing. At that time, it was using Web Services -- hence the name -- and not REST APIs.