The wikipedia article starts with the introduction of mainframe-based LANs in the 1950s. They then describe how the TCP/IP format was created some twenty years later in 1974, and how the military managed to get two different LANs to communicate with this format in 1977-1978, leading to the exclusive use of TCP/IP by 1983. Only military, government, and university researchers were allowed to use it. Commercial use was forbidden. In 1984 the University College in London started using it for trans-atlantic communication. Between then and 1988 CERN began switching over to TCP/IP. Europe remained opposed to TCP/IP and was isolated until 1989. By 1992 universities in east asian had also switched to TCP/IP.

The first internet service provider (ISP) opened for business in 1986 but there was alot of opposition from universities to non-educational use of their networks. In 1994 restrictions on commercial use of the internet ended. After that there was a dot.com boom that lasted for 6 years, during which the number of ISPs exploded. This is where I come in, because IMO that's when the real internet began. Until 1994 it was just a bunch of LANs connected together and only certain people had access.

But before public internet access there were individuals with modems who exchanged data unimpeded over the phone lines. No servers required. Even today there are still fax machines and cell phones. Do they use TCP/IP ? I don't really know, but I doubt it. Way back in the early 90's before ISPs really got going when I had a part-time office job, my employer had a single large commercial fax machine with about 200 phone numbers programmed into it. My job was to stand in front of it all day and send faxes. Lucky me. That's a damn big commercial network, and it wasn't even connected to a LAN.