Right, you feel that God does not exist but the truth is you don't have any evidence that support this.
See my previous post about IQ.
You feel that God does exist, but the truth is, you also don't have any evidence that supports your belief. You have a bunch of notions that could have many, many explanations, but you find it quite sufficient to presume that "God" is the only answer, when in fact that is simply not true. That doesn't stop you believing, but that's okay, because believing is a very different thing from knowing. I allow you your belief. Why do you not allow others theirs?
Now, as to the business of "no evidence to support the non-existence of God" (or anything else, for that matter). If I make an assertion that something exists...let's say a leprechaun or Bigfoot. Now, if you don't believe me, what evidence could I produce to convince you? Well, most obviously I could just haul one in at the end of a leash and say "see for yourself." What else, I don't know, but you if I couldn't produce anything at all, you would be well within your rights to say "sorry, without evidence, I don't believe you."
But now, what if I say to you, "you feel that leprechauns and Bigfoot don't exist, but the truth is, you don't have any evidence to support this." What evidence are you going to bring to prove your non-belief is true? The answer is: you can't. It is impossible.
The difference with a positive claim (like God exists) is that it takes only a single example to demonstrate such a positive assertion ("there is a dog in this room," requires pointing to a single dog, and the argument is over). The inability to give examples for a negative claim ("leprechauns don't exist") merely shows that you have not yet found or noticed any, but not that they do not exist, somewhere, hidden in ways you don't yet understand.