I've found it surprisingly difficult to pin down the early history of distributed file systems. The first reference I can find to Sun's NFS is a paper presented in 1985, when the software was already working and deployed. A few years later, when we started buying Hewlett Packard workstations in Manchester, Sun was urging other Unix vendors to include NFS with their Operating Systems, and HP were encouraging their customers to switch to NFS from the HP system, which I never tried myself. (It was called Remote File Access, or something like that.) The success of NFS is one example of the success of open standards in software.
In the same year 1985 I find the first paper referring to the AFS file system, the immediate ancestor of Coda and several other closely related file systems. AFS was developed (under a different name) at Carnegie Mellon University in Pittsburgh, and soon after 1985 its name was changed to 'the Andrews File System' (after Andrew Carnegie and Andrew Mellon, the two patrons of Carnegie Mellon University). CMU spawned the Transarc Company to develop and market AFS.
I don't know exactly when the other network file systems arose, but I doubt any of them were earlier than NFS or AFS; some of them of course arrived on the scene much later.