Assuming "God" is sensible in some way, by what criteria are we able to tell illusion from non-illusion?
You've also implicated that sensation is not a proof of existence. It appears you've committed yourself to a fairly hard skepticism ... which, to avoid, brings us back to the question of criteria.
Contradiction is, to a large degree, a matter of interpretation. Moreover, there are two forms of contradiction; formal/ostensible/logical (Hilbertian, I call it) and material (Fregian). The first is simply an assessment of the immediate logical form, while the second requires an analysis of the objects in question, in order to make sure that they don't imply a tacit contradiction. This is where interpretation comes into play. Though, in any case, if something is formally immaculate it won't be by necessity true. An argument in which every inference is valid would not necessarily be sound, nor give true conclusions, if the premises themselves are untrue. In a similar vein, unsound arguments with false premises can render true conclusions through invalid inference.
I think it depends on standards of proof. But the best (and probably first) test of validity and truth we have -- the principle of sufficient reason -- is one of utility. In short, the reason we think the big bang happened is because the assumptions that lead us to believe it happened are very useful to us. That said, in these fields we don't and cannot have 100% confidence in a strictly theoretical setting -- there never can be when it comes to induction --; for a science will and must change its assumptions in the light of new and good evidence, where religion may not. That science shouldn't/doesn't pretend absolute certainty is perhaps one of the more important defining characteristics that sets it apart from a vast majority of religion today.
On the contrary, if we had no way of accepting the absurdity, everything itself would appear absurd and purposeless. To this extent, my God is of every form of "use" possible.



We all are the creations of one Lord my dear!