There are some seemingly well constructed arguments for the existence of god utilized by apologists in their quest to rationalize their religious beliefs. The three classic apologist arguments are the:
1) Teleological Argument (Argument from Design)
-Basically, there exists order and complexity within nature, and order and complexity, ie, design, is contingent upon a mind. This mind is god.
2) Cosmological Argument
-Basically, finite entities must have a cause. You cannot have an infinite causal loop/chain, in which something created something created something ad infinitum. There must be a first cause. This first cause, by definition, is not contingent and is not an effect.
3) Ontological Argument
-Basically, and laughably, it asserts, a priori, that if you can conceive of the greatest possible entity, then said entity must exist, since existence is superior to nonexistence.