It is not possible to show concrete evidence for supernatural phenomena. All I can do is offer possibilities and likelihoods to help you discover the truth.
You at least need some reasoning or some evidence in order to construct plausible possibilities and likelihoods. If there is nothing to support an idea at all, it is (at best) a guess.
The key word here is interacts. To interact, the brain needs the freedom to exert its own will. But this is not possible in a deterministic world where it can only react.
You are still very confused about the material / deterministic / free will questions. I am forced to wonder if you've ever actually thought about it at all.
Logically there is no connection between material and determinism - the physical world may be deterministic or it may not. Since this "non-material" world of yours seems entirely without supporting evidence, we can't say whether that is deterministic or not, either.
Which of the worlds you place the bit of us that does the decision making, therefore, makes no difference; you can still only use deterministic and random elements.
Understanding how free will and conscious awareness might work is difficult but your approach seems to one of enormous self-importance and incredulity: I can't possibly be made out of all the stuff we see around us (despite the evidence that we are), so I must consist of something else, that I'm going to call
magic non-material - and I won't bother to consider if it would actually make any difference.