Proving A Negative

A revelation I've had recently regarding substantiating or disproving claims is whether or not one can prove a negative claim or that something doesn't exist. In general, it isn't good argumentation or reasoning to try and prove a negative, or to formulate an argument that something doesn't exist and try to "prove" that it doesn't exist. This is because, for example, if one tries to argue that God doesn't exist, there could always be another god around the corner that one is unaware, or if one tries to prove that leprechauns don't exist there could always be a leprechaun, however unlikely, hiding somewhere in the corner of the universe.

What is better, and provides for better argumentation and reasoning, is to make an opposite positive claim which would necessarily entail that assumption, which can met with a burden of proof. Instead of simply making the claim that the Christian god doesn't exist, one could rightly claim that the Christian god is a mythical figure made up by men and provide evidence that supports that assertion. If this claim is justified this would obviously entail the assumption that the Christian god doesn't actually exist as an existential being in our reality. Several lines of evidence could be given to support this assertion, such as the nature of god in the Bible reflecting the nature of man, how the Bible seems to be anything but divinely inspired by an omnipotent supernatural god, the millions of unanswered prayers, etc.