The single best thing to keep a path open in a wild garden is to walk it on a consistent and regular basis. Other than that there are no magic tricks to replace routine maintenance. In the growing season that means weed whacking the paths if necessary. In the fall and winter that means raking or blowing off the leaves.

The more you walk it picking up sticks and editing out aggressive smothering plants in the surrounding hillside, the more it will become a garden.

Thanks Christopher, I haven't had a wild garden before, so this is new to me. Perhaps that explains why there were no pavers or anything installed to make paths. Since the walking areas do have landscape fabric (much of it torn), is it an indication that it was installed and walked upon bare, or would it have been covered with mulch or something similar?

Landscape fabric in what are obvious paths would most likely mean they were covered in mulch. Gravel can also be used in woodland walkways. Neither of those will prevent weeds permanently. Rocky hillsides are not very conducive to cement or paver paths without a great deal of expense so it seems they used what was available to define the paths, free rocks.

Let me add that making a garden of a natural landscape is not so different from making a typical suburban garden. It requires the active participation of a gardener, a person who cares for and tends the land. The methods may be slightly different, less intrusive and in many cases easier, but it is still active management of the landscape. Neglected and ignored, the forest will take it back in the blink of an eye.

You might find my walk into the deep forest yesterday of interest. http://outsideclyde.blogspot.com/2020/04/where-caged-orchid-still-blooms.html