Our evidence for no God is primarily the lack of evidence for a God. Now, it is true, that absence of evidence is not evidence of absence. But God has the same amount of evidence as a unicorn...but you don't believe in unicorns until you see evidence right?
What about Superman? Seen any evidence of Superman? No? Does that lack of evidence tell you he's real or fake? You know he's fake. What about Hogwarts?
Let's take it up to the next notch - if at least one God is real, how do you know WHICH? Each religion says it's right and others are wrong. So at most 1 religion of the tens of thousands in existence today can be right. None have even a drop of evidence for their God being real.
And if God were real, why would he MOSTLY hide, but then only contact us in vague and imprecise ways? Why would God communicate only through prophets and thousands year old scriptures? If God wanted to be worshipped, wouldn't he communicate clearly, in ways not open to interpretation? And if he's good, as is usually claimed, why would he send people to hell for the mere 'sin' of not GUESSING correctly in this multi-religion lottery?
Logically, he wouldn't. Honestly, we can go on and on and on with this. God just doesn't make SENSE any way you look at it. His purported actions are illogical. Why would God create homosexuals and then order his followers to hate and kill them (make no mistake, the bible EXPLICITLY orders the death of homosexuals). Why would God approve of slavery as the Bible does? Why would God create man so badly that he needed to kill all of them except Noah's family? Isn't he all-knowing? How could he have goofed so spectacularly?
No seriously, we could do this for hours. I'll stop here.