I think a good argument can be made for the existence of God based on the existence of the universe. We know the universe began to exist. Given that whatever begins to exist requires a cause external to itself to bring it into existence, there must be a cause external to the universe to explain why it came into being. Whatever brought time, space, and matter into existence cannot itself be temporal, spatial, and material, and thus the cause of the universe must be eternal, non-spatial, and immaterial. Furthermore, the cause must be personal in nature since there are only two known sources of causation—events and personal agents—and it is impossible to explain the first event in terms of a prior event. Therefore, an agent must be the cause of the universe. A personal, eternal, non-spatial, and immaterial being is what most theists mean by “God.”
While I think this argument demonstrates the existence of the divine, it cannot tell us anything about the number of divine beings responsible for creating the universe. There could be one, or there could be billions. An additional argument is needed if one is going to prove the existence of one and only one God. In the past I argued for monotheism on the basis of divine omnipotence. I reasoned that the property of omnipotence cannot belong to more than one being, for if two or more beings have to share power, then neither being can be said to have “all” power. So God, then, must be one if He is omnipotent.