I've shown you from Genesis that the soul immediately impacted the flesh.
No you haven't. You showed me sin impacted the soul which affected the body. I showed you where the sin nature now is to be found but you deny it. You confuse effect with affect. The effect of Adam's sin causes us to be born with a sin nature which is found in the body which in turn affects the soul and body.
The serpent acted the way the sin nature now acts by presenting an "anti-God law". Adam had no sin nature so needed an external "law" to start the ball rolling. We have an inner law that sets things in motion.
Romans 7 is quite clear where the anti-God law resides.
Romans 7:23
But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members.