1. Cantor worked with infinities in mathematics. He even concluded that the highest number was not infinity but infinity within infinity. We can not demonstrate that universe itself is infinite given our always finite time-line or life, that never catches up with some kind of infinite space, time, mind, matter.
2. You might attribute infinity to God. You might attribute a supreme mind to God. You might attribute God with the being of the greatest good. The greatest, the supreme, are adjectives, working to put this being into a mathematical expression, but only achieve this with simple superlatives. As you can from this, a state of being might be mathematic, not just in geometry.
3. Inherent structures in the universe might indicate that their is an intelligent designer, but it also may mean that within the universe these structures naturally exist in the dormant and the actual.
4. We have more proof that the universe is exogenous, having no external cause, than it having an external cause.When we trace back in time the inflation of the universe, through various tracings of evidence, we reach a theoretical point of expansion. There is a theory that the expanding singularity is no more than the inverse of a gravitational singularity (black-hole).
It is possible to resolve the problem of causation of the universe by thinking of the universe is a cyclical rhythmic eternity (cosmological problem). Where is intelligence role in this? Intelligence is also in this, as too may be a being in another universe who has the likeness or attributes of what you yourself or others may call a God or the God.
God has been said to be, "The Alpha and Omega." It might be than, that in a universe with different mechanics there is some kind of omnipresent intelligence. We can only prove there is intelligence by its reduction into the physical beings and the life that exists in our observable worlds.
5. A creator being causing the universe outside of the universe, is something like a creative developer designing a virtual reality. Some might think of this being(s) as only a reality developer, others might think that he or it is living out the life and the spirit, animating and giving intelligence to animals, sims, and avatars.