We have two types of evidence. One is the evidence produced from our physical senses, man made equipment and human logic. The other evidence is the perceived nature of our human mind.
Okay.
It is apparent to most people that the former does not adequately explain how the latter exists.
Even if you had evidence that this is true of most people, it would be an ad populum fallacy.
We have yet to discover what makes the human mind work as it does.
Exactly; which is why we cannot definitely say whether it can or cannot be explained by current science.
There are some who assume that material science will eventually explain how the conscious awareness and free will of the human brain works, but this is only an assumption based upon the logic that nothing else exists apart from what can be detected by current science.
Science is the only way we have of investigating the problem - if you have another methodology, then feel free to present it. There is no assumption that
current science will do the job. Some serious scientists have argued that new theories will be required, but they remain in the minority.
My own view is that human science may never be able to discover the nature of our human soul. I maintain that the evidence for the human soul lies in the awareness of our own existence and our ability to implement acts of free will rather than the limited scope of human scientific investigation.
You are entitled to your view but you have not provided any evidence or reasoning to back it up, so it no more than blind faith.
You really need to examine what you mean by 'free will' as well. Most people (in my experience) have a concept of it that is self-contradictory.