By definition, no. Quick and summarized disproof which shows the impossibility of god:
God is a supernatural being. Supernatural, by definition means outside of nature, meaning that anything properly defined as supernatural cannot interact in anyway with the natural world. We cannot, by definition, even KNOW about anything supernatural. Therefore, any supernatural being in the public consciousness is fictional by definition, otherwise that being is not supernatural.
And so on. Such disproofs can be applied just as easily to any other characteristics normally attributed to a god-like being: omnipotence, omniscience, being worthy of worship, being greater or more perfect than anything else, etc. Other characteristics like absolute benevolence and absolute justice can be similarly proven to be irrational. Which then leads to the obvious only remaining scapegoat: God isn't logical. Which can then easily be broken down to the believer being clinically insane and such, as there is no longer any reason to have faith in something you can no longer even define or imagine.