It depends on what you mean by "clear and demonstrable." I don't think anyone can demonstrate. On the other hand I can give an example of an experience.
Long story short, about ten years ago I was investigating faith and reading some faith-related material while at a diner. As I was leaving I saw a homeless vet nearby, and being somewhat motivated by the teachings I had been reading, I wanted to help, but not knowing if he even needed anything, I decided to just have a chat with him and find out what might happen. He was a little difficult to talk to, but soon I was stuck listening to him ramble on about war stories which seemed to go on forever, and without a chance to politely end the conversation. Eventually, an older woman came up to both of us. I think she was curious, but in a few moments, for reasons I didn't comprehend, she said "I think this is a divine appointment." I didn't think much of it, and I took the opportunity to politely part ways.
Over the next decade I basically wandered through life semi-haphazardly. More recently, I found myself contemplating the subject of the fore-ordained will of God, not exactly studying theology but basically trying to understand the subject. It was at this time that I was invited to have lunch with a relative, who is also an older woman, and toward the end of our conversation, she said "I think this a divine appointment," and suddenly, it triggered a recollection of memories spanning years, to the point of the first occurrence, and in such a way that it congealed as a realization that I had just experienced a fore-ordained event for myself, providing an answer to the problems I was struggling to understand concerning the same subject, and the timing couldn't have been better.
Later, I came to see this as what others have referred to as an "epiphany," and I'm inclined to think that God is active in the world, but most people usually just don't understand what ancient peoples were describing. God could be active in peoples' lives, and they might not even realize it.