The burden of proof lies on the shoulders of those claiming something exists, not the other way around.
There is still a burdon of proof placed upon those making a negative claim. You are falling back on the argument that if you don't see it for yourself, it can't be real. The Egyptian philosopher Aesop wrote a very good fable on this. I will try to recall it as best as I can.
There was a boy in a small village, who went out one day to watch the crows along the Nile. One day while he was looking, he thought he saw one crow that was white, instead of black. Filled with excitement, he ran back to his parents and exclaimed to them "Mommy! Daddy! I saw a white crow by the river!" His parents both frowned at him and shook their heads. "Son, there is no such thing as a white crow. All crows are black." The child wouldn't budge. "But mom, I SAW a white crow with my own eyes!" Angry at their childs defiance, they punished him and sent him away. The next day, the boy went back to the Nile again, and this time I managed to see the Crow up close, and he spoke to it. "Are you a crow?" he asked, unsure of what he was seeing. "Yes, I am a crow," the bird answered. The boy, now torn between what he sees with his own eyes and what his parents taught him, spoke again. "I thought all crows were black," he said. "I know, " the crow replied, "but I am white. I am the only one like me that I have ever seen." The boy at once ran home, and exclaimed to his parents "Mommy! Daddy! I saw the white Crow again!" His parents, angry that their child did not accept their word, punished him far more severely.
I can offer you no proof God exists accept that God is real to me. You cannot in turn, offer any evidence that God DOES NOT exist, accept that you cannot find any. In science, a lack of evidence has NEVER foreclosed the possiblity of the existance of something. It only states that a conclusion cannot be drawn. By stating that a lack of evidence leads to a conclusion, you aren't following science very well. This is the point I am making when I say that you bear a burdon of proof, and I can indeed turn all the arguments you are useing on me against your own claim.
Seccularist: "God does not exist."
Theist: "Really, why do you think that?"
Seccularist: "Because it is true."
Who bears the burdon of proof here?