Fooling God into Showing Himself

The Economist, as well as others, have been spending quite a bit of their attention recently on religion (I last wrote about this, with links, here). They now tell of a EU research budget dedicated to research projects designed to find God. Actually, most of them seemed focused on finding why people believe in him. Some of the researchers are looking at flashes of lights on maps of human brains, others are trying to find economic justification for religious behavior, or social justification, and what have you.

This is all well and fine, and personally I'm all in favor of science, at least if it's good science (as against quackery). Still, it seems to me there's a glaring lack of logic common to all the projects described, and I mean all of them - and it's a problem of neutral logic, not of lack of religious belief or fervor.

Let's say, for the sake of argument, that when the various scientists talk about religion, they mean sets of beliefs that start from the assumption that somewhere "out there" there's an infinitely wise and boundlessly powerful entity, that also just so happened to have created us, even while leaving us the freedom to think as we will, including to believe in him or not. By definition, this entity (God) would be a bit ahead of us humans in knowing what flashes will appear when in which segments of the brain, or what statistical chances which sets of behavior would yield in which results. Wouldn't this then logically mean that there is no way in which God could be "tricked" into being pinned down by whatever empiric experiments?

Put otherwise, doesn't this mean that only non-believers can expect to set out on a track of empiric experiments designed to lead them to the divine entity they don't believe in?