The specific issue is: How does any evidence disprove Genesis ?
Well, this is really too imprecise for discussion. What are we trying to prove/disprove about Genesis ? The very specific assertion that it has scientific content? Or the more general assertion that it has some sort of epistemic content ?
I'm assuming you are referring to the former, but correct me if that's unfounded.
However, the question of whether, and to what extent, Genesis has scientific content is far from settled within the Christian community.
According to my worldview, anyone who does not believe that God is the Creator is irrational/insane. But my worldview admits that philosophy is king unlike the scientific methodologies pushed by Razd/Ned which also rely on persons being rational. The issue is their refusal to admit this which makes their claim about their conclusions being based only upon evidence absurdly false.
Yet the conclusion of YEC from this assertion is a non sequitur. Even if we grant its points in toto, which I'm prepared to argue we should not.
It is quite possible to believe God created the universe through primarily natural process over billions of years. Indeed this is the majority Christian position.
I think you've assumed a burden of refuting this by primarily scientific arguments, if this topic belongs in this forum.