Interesting historical facts according to https://www.edn.com/electronics-blogs/edn-moments/4395946/Stibitz-demonstrates-remote-computing–September-11–1940:
George Stibitz of Bell Telephone Laboratories used his Complex Number Calculator (CNC) to demonstrate remote computing for the first time on September 11, 1940.
Stibitz was among a handful of engineers across the globe designing machines that involved using relays to implement binary logic at the time. You can read more information on them at computer museum site.
Keep in mind that the famous Turing Machine paper was published just a few years earlier.
We had to wait few decades for modern networking to start to develop. One historical event was this: The first-ever computer-to-computer link was established on ARPANET, the precursor to the Internet, on October 29, 1969.