Does the Theistic God Exist

Note: This is not a debate on the existence of God in general, but rather, the existence of the theistic God. 

The topic of the existence of God has been the subject of fierce debate for as long as humanity has existed. Though many arguments have been developed, mankind has yet to reach a definitive conclusion on the matter, and probably never will. However, it is still productive to discuss the evidence for and against the existence of the theistic God in order to reach conclusions as individual people. My opening statement is by no means designed to be an exhaustive argument for the theistic God, but rather, just one argument among many.

The very fact that the universe is should cause us to ask the question: When did the universe begin? Knowing that time is a measurement of duration of existence, can we answer this question with a definitive timetable without appealing to something outside of time and matter? In this debate, I will be arguing the negative position, that we absolutely must appeal to something outside of time and matter in order to define when existence became. This 'something' is what theists call God.
The Principle of Sufficient Reason(PSR) states that everything in existence must have a cause. This is the basis of scientific thought; explaining the 'whys' and 'hows' of events that occur. How does an object fall when it is dropped from a certain height? The simple nontechnical explanation is gravity. Why does an apple fall from a tree when the tree is shaken? Because of force of motion, or the properties of mass and acceleration altering the current state of said object. PSR is used in practically all scientific thought, and thus, it is proper to conclude the universe had a first cause. 
Atheistic evolution cannot explain existence, for it has no first cause. There was a big bang approximately 13.8 billion years ago that caused our universe to exist, the atheist will claim. The simple question is this: where did this big bang come from? What was its cause? How much time elapsed before this event occurred? Without definitive answers to these questions, one would have to fall on one of two positions. Either the universe is eternal, ie had no beginning, or there was a first cause which set the universe into motion. (In order for this cause to truly be a first cause, it would have to be the uncaused cause of all other causes.) The universe cannot be eternal, for if it were, there could be no timeline with which to measure its existence. This violates the foundational concept of PSR. So, this leads back to my main question: If there is no God, no uncaused causer of all things, then what caused the Big Bang? 
I propose the second of the two possibilities I listed above; that there is indeed a first cause which set the universe into motion. Just as a string of railway cars cannot be set into motion without a first cause, ie, the locomotive, neither can the chain of causal events that led to the creation of the universe be set into motion without a first cause; what theists call God.
A possible objection to this argument may be that the existence of the theistic God violates PSR in the same way atheistic evolution does, since God is not caused by anything, however, this is rooted in a fundamental misunderstanding. It must be noted that the Big Bang is a chain of causal events, that is, it is not an uncaused causer, but rather a string of causes ultimately resulting in the universe we see today. It is not so with God, for God is existence itself, and thus is the cause of all things that come to exist.
So, to restate the argument:
(a) PSR states that everything that claims existence has a cause.
(b) The universe came into existence at a certain point in time
(1) Therefore the universe must have a cause
(c) The universe cannot be its own cause, for the Big Bang is a chain of causal events which produced the universe
(2) Therefore there must be a first cause which caused the causal events leading to the creation of the universe
(S) This first cause is what theists call God