Well, massive communications networks have been a thing since at least the 1930's (mostly with telephones and radio), and telegrams from the early-19th century are the earliest attempts at global communications. During World War Two, various Allied military forces were trying to develop a computer-based communications network (which is essentially what the Internet is), and futurists were predicting that people would use computers to shop and commune from home back in the early-1960's. Also, Mark Twain actually talked about something very similar to the Internet in one of his books back in the late-1800's. So, I guess the 1970's and 1980's was when people were sure the Internet would soon be a thing.

I doubt that they would have ever expected memes, though.