Whatever begins to exist has a cause.
The universe began to exist.
Therefore: The universe has a first cause.
1. Whatever begins to exist has a cause - false. It is certainly our common experience that this is true, however the birth of a universe is not a common event. It has been demonstrated that in empty space particles are constantly being born and annihilating each other purely randomly and without cause. It is entirely possible that the birth of our universe mirrors this phenomenon.
2. The universe began to exist. - Unverifiable. It certainly appears to have had a beginning in the big bang, but there are a number of ideas about the big bang (i.e maybe it was a "big bounce") that don't require a time zero. It's entirely possible that the universe had no beginning. If you dispute this fact, then I would dispute that god had no beginning and challenge you to demonstrate god's "first cause."
3. Supposing that points 1 and 2 are correct, how does something necessarily having a "first cause" suggest an intelligence of any form? If anything, it simply suggests that our picture of the universe is incomplete, which I think just about any physicist or cosmologist will readily agree with. Simply pointing to a gap in knowledge is not sufficient evidence for belief in anything. Let alone a god with the power to create an entire universe.
