Sure you can in many instances. I can prove I don't have a pistol in my front left pocket by turning the pocket inside out. In this instance, however, you can't prove or disprove the existence of God. This is by definition as God transcends the empirical bounds which restrain the concept of "science" or "reason". "Finitum non capax infinitium." Each side to the argument must rely on trying to establish the greatest probability for their position.
No scientist,or group of scientists,will ever be able to prove...or disprove...the existence of God.
Perhaps I should have said that you cannot prove a negative by logic alone. By demonstration (e.g. turning out your pocket) you can negate a positive statement of fact ( in your example, “you have a gun in your pocket”).