The Mysterious Cave is an aquatic pathway which connects Route 316 and Huron Town together. Despite its appearance on the Vesryn Region map, it is not accessed through Caspian City. As it requires Dive in order for it to be navigated, the Mysterious Cave can only be explored once the player has obtained all of the Badges of the Vesryn Region.
Assuming that the player doesn't somehow lose their bearings after facing a wild Pokémon in battle, this area is fairly straightforward to navigate through and is completely devoid of random trainer encounters. The player simply needs to Dive below the water in some sections and resurface in others, entering additional cave entrances and pathways along the way.
Eventually the player will reach an area where the weather changes to rain, which will be the first major indicator that they have arrived in Huron Town.