I know it's always hard to define an exact first, so I'll just ask about early network file systems. To be more specific, I'm wondering about file systems that transparently present directories and files as if they were local. I don't consider FTP or similar mechanisms to be candidates.
For some time it has been my suspicion that the ITS "MLDEV" facility was very early ("the first"), but I never had any facts to back it up. I do have a file timestamped November 1972 that gives us an upper bound for the introduction of the facility. On the MIT-AI PDP-10, it provided an ML device (hence the name) which worked much like the local DSK device except the data was accessed through MIT's ARPANET IMP. MIT-ML of course had an AI device.