What do you mean by 'supernatural' - and (assuming your definition is the standard one of 'not detectable by any measurement') by what mechanism that could possibly affect physical matter? (the onus is on you to prove the positive claim that there exists the supernatural or soul to begin with, which there is currently no evidence for).
The concept is self defeating by its own definition, either it is physical in some capacity (and therefore can be measured and replicated through yet unknown means) or it is not (and therefore indistinguishable from not being there at all).
Feeling that there 'must be' a soul is not enough to prove that it exists.
The feeling of experience is not enough to prove that experience is in anyway supernatural.
> What is impossible is to replicate a soul with purely physical matter.
What? Why? Where is the proof of this?
First and foremost, I'll give you an in. There is a difference between material, and processes like waves, waves I would argue are non-physical things manifested in physical material: you might want to start there.
But all roads lead to Rome from that line of thinking too, so you might need to come up with something far more clever.