IIRC before that Unix had directories, but it wasn't a rooted DAG. I don't recall the specifics, but I suspect you had to know a directory's inode to get to it if you couldn't reach it from where you were.

It was a general graph. Any directory entry could link to any inode. Standardize ., .. and forbid links to directories other than those and from the directory they're in and you get the classic UNIX file tree.

Multics, the predecessor to Unix, was the first OS to use a hierarchical file system. Before that, file systems were typically flat: a single long list of files.

I don't know how the original Unix was, but presumably flat.