How do you know that Allah is the only God and in fact even a God?

Yes you are right that The Qur'an says that Allah is existence there is no god except Allah. We muslims know and believe in the existence of Allah because we have strong eeman and taqwa and we covince its existence through seeing and watching Allah's creations this universe and all of its contents Muhammad pbuh and his parents were not the members of the cult of ancient sumerian people.Muhammad pbuh and his ancestors were descendants of Ibrahim prophet from his son Ismael prophet who believed in tawheed religion just to one God that is Allah..(monotheism)