Short answer based on positive evidence that shows the direct evidence for God in a laboratory is no.  The argument goes that one can stop thinking and substitute the point of not knowing with “God”.  For example, in the past the question was asked, who moves the stars and sun in the sky?  Thinkers believed that it was God who directly moved them.  But now we know this is not the case.  The argument extrapolates that, just as it was said of lightning, earthquakes, and other mysterious phenomenon, where science had or has not yet discovered the cause or reason, then God must be that cause or reason.  

The longer answer, however, is that “existence” is a logical concept that falls short of describing the God.  Is God imaginary?  Even if the answer to this is yes, who is the one thinking of the image, or imagining the fantasy?  The mind of man is greater than anything real or imaginary that we contemplate, because contemplation is contained within the human mind (or within brain if you are a monist).  Since the mind is greater than anything it is able of imagining or contemplating, can we be so arrogant as to dismiss the existence of Something (i.e. God) that is outside of (i.e. above, beyond) imagination or contemplation?

It is possible to state that God does exist if one is aware that language and logic are both limited and fail to approach God.  After all, language is used to convey ideas of something else that it conveys.  It is impossible to realize an Unseen Reality (i.e. God) through the powers and senses of man, if God is pure and holy above the reach of doubts.  Because anything we can reach by our powers and senses, we can doubt.