The WWW that was created to share scientific papers? Or you mean the GP's Internet that was created to organize the US troops on the event of a nuclear strike?
I guess so, there was plenty of people aware they were not toys. Most of those people did use them as toys most of the times, like everybody else at the time, but the toy classification was mostly from uninformed people and trolls.
While working at RAND on a scheme for U.S. telecommunications infrastructure to survive a “first strike,” Paul Baran conceived of the Internet and digital packet switching, the Internet's underlying data communications technology. His concepts are still employed today; just the terms are different. His seminal work first appeared in a series of RAND studies published between 1960 and 1962 and then finally in the tome “On Distributed Communications,” published in 1964.
https://www.rand.org/about/history/baran.html
Baran's original packet (block) switched networks development papers, and in fact his entire catalogue, are available at RAND:
"On Distributed Communications I. Introduction to Distributed Communications Networks"
https://www.rand.org/pubs/research_memoranda/RM3420.html
(This and the others are listed at the first link.)
Most of the citizens of the western world (even those with a degree) definitely pidgeon-hole expensive university projects as "toys", because they don't have one and don't see a need for one.
Academia is a weird place and is often underestimated.