Following the lead from this answerfrom this answer. And reading page 2-15 from the manual from Bitsavers (thanks @grawity).
Shared Data
The second design principle of the Domain/OS distributed file system, sharing by default, implies a global uniform name space. The name space of the distributed file system appears to users like that of a giant timesharing file system. It is a traditional UNIX hierarchical name space, except that absolute pathnames can begin with the name of the network root (called //). It is also possible to express pathnames relative to the root of the local node (the / directory).
There is also an older manual from with a "First Printing: July, 1985". On page 1-4:
The double slashes (//) in Figure 1-2 represent the top level of the naming tree, the network root directory.
So, we have confirmation that Domain/OS from Apollo used // for network root.