Some jinja were founded at particular times by particular people, and we have clear records of who and when. Others, however, developed naturally, and the oldest jinja are believed to fall into that category — even the ones, like Jingū, that have very mythical foundation myths. It is natural to think of this process as something that happened in the distant past, and not today. That may not be entirely correct.
The August 14th issue of Jinja Shinpō includes an article about a very interesting process.
During the pandemic, a jinja in northern Tokyo, Tenso Jinja, set up locations for distant reverence (yōhai) of the main sanctuary, so that people would not all crowd together near the sanctuary. (That in itself is an interesting approach that I have not seen at other jinja.)
At the same time, the priests set up a location for paying distant reverence to Mt Fuji, indicating the direction to face (as it is not normally possible to see Mt Fuji from Tokyo these days). The priests noticed a lot of people paying their respects in the direction of Mt Fuji, and so they added a sign board, and set up shimënawa to mark off the area. Last year, they also added a monument in memory of the former chief priest, and named the area “Higurashi no Mori”, which means “Cicada Wood”, because those cicadas are said to have been singing on the day the former chief priest died.
These developments led people to think about holding a matsuri at the site, and that was the occasion for the article. They invited people with deep connections to Mt Fuji, and held a “Fuji Matsuri”. The people invited included the head of one type of Sect Shinto, Shintō Fusōkyō, which has a particularly strong connection to Mt Fuji.
After the matsuri, the current chief priest, Revd Kobayashi, commented that she (probably — the given name is much more likely to be feminine) felt that locations became sacred as people piled up veneration there, and that the location was likely to become a subsidiary jinja at some point. “It feels as though I am experiencing the process of founding a jinja for real,” she said.
The hope is that the Fuji Matsuri will be held again next year, so maybe a new jinja will be born there.
Another interesting point about the article is that it consistently talks about venerating Mt Fuji, the mountain, and not the kami (Konohanasakuyahimë) who is most commonly associated with mountain these days. I think we should probably take this at face value: the mountain is the kami, at this location.