The Internet has been running since 1969 (Arpanet).
Truth: What happened was there were military-inspired studies in the early 1960s of how to built a robust network that could survive attack - notably first-strike nuclear attack. The answer is to decentralise everything, including addressing and routing, to have no essential HQ, and also to have redundant paths.
Major US academic research centres (including military research bases with links to academia) took this idea in the late 1960s and built the Arpanet network that eventually evolved into the Internet. It was full of scientists and university academics from the start.
The Internet was originally set up not for email, not for sharing papers, documents or programs, not really for user communication at all in fact, but rather to allow sharing of expensive hardware (run programs remotely on someone else's expensive federally-funded computer).
Email
was a surprise when it took off on Arpanet
in the early 1970s.
Later, email discussion lists started, and the
usenet
decentralised discussion-group system,
1979.
File sharing would be done between sites when they worked together on a project. Later came the concept of a permanent archive of files that anyone on the network could access at any time. Archives of programs were set up, and later archives of documents of all sorts. It was not until the mid-1980s that it became clear that an embryonic electronic "library" of documents was starting to be built up online. Now, of course, the library has billions of documents.
Internet had steady growth and usefulness through 1970s, 1980s, and early 1990s, but did not really take off until Web idea invented.
As late as 1992, the Internet was being ignored by most of the world, including even much of the computer industry. But every computer science undergraduate lab in the world was full of people glued to it.