I know you said you're addressing non-believers more so than believers in God, but I wanted to add my two cents. When people claim there is no evidence for God, I wonder just how much evidence they need, or what kind of evidence, or even how do they define evidence?
Because for me, looking at the vast complexity and interconnectedness of nature and the cosmos is actually plenty of evidence that there is some sort of intelligent Force beyond us. And lately I've been studying natural law and first principles and the existence of these, regardless of time in history or culture, seems like enough evidence that this original Force also is just.
So even though I struggle with organized religion and do not accept scriptural authority, I find plenty of proof for the existence of what I call God. The evidence in looking at is equally accessible to everyone, regardless of religious affiliation. But there's also the psychological factor you must account for that people will see what they want to see. They will find what their looking for. That applies to me as well, but not any more than to atheists. They don't want to find God, so they dismiss the evidence all around them. That's their perogative. But let's not say there is no evidence. The evidence is there. Perhaps we all interpret it differently to get to our preferred positions, but the evidence is there.