Also, if you postulate that everything has a cause, then the chain of causality must extend infinitely into the past. But an infinite series cannot exist in actuality, so a first cause, or Uncaused Cause, must exist.
Exactly. This is the problem atheists have. You eventually arrive at an uncaused cause, which must transcend our universe. The only two things fitting that description are mathematical objects, or an unembodied mind.
From our observations, we have no reason to believe that numbers or theorems have causality. The number seven cannot cause anything. This leaves us with only one explanation. God.
There can be very legitimate debate on the nature of God, how he interacts with his creation or if he does at all, but I think deductive reasoning leads to a higher power.