How on earth to the PCs come up with a mystery and what it's resolution would be, and then go about the process of solving it? That would be like writing a crossword puzzle for yourself then sitting down to complete it.
In my campaign, the druid began drawing parallels between the locations they had traveled and the four elements. He suggested that the ritual the cult was performing required actions in keeping with the four elements. He was completely wrong, but if I hadn't been focused on using the published material, I could have incorporated that into the actual story.
This is how you run a game that the players write. Listen to what they guess is going on, take that, and add your own touches. You don't have to have the whole story written at the start, you just need hooks to hang the pieces the players author.