The prominent, and highly articulate Christian philosopher, William Lane Craig, has numerous resources for defending the Christian faith. You can find many of them at his website: http://www.reasonablefaith.org
Craig's famous kalam cosmological argument (KCA) for God's existence has been perhaps the most highly discussed argument for God's existence in the past thirty years. The argument can be summarized as follows:
1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.
I won't spend time on every detail of the argument. However, Craig defends (1) by metaphysical considerations. "Ex nihilo, nihil fit" - out of nothing, comes nothing. Another way of putting this is that being cannot arise from non-being. In fact, if literally nothing existed, then not even the potential would exist for something to come into being. Hence, if the universe came into being at some point in the finite past, then something must have brought it about.
Craig offers four lines of argumentation in favor of the second premise, what he considers the crucial premise of the argument. Two of the arguments are philosophical, and two are scientific. I will spend my time solely on the second of his philosophical arguments.
1a. An actually infinite series of things cannot be formed by successive addition.
2a. An infinitely old universe is a formation by successive addition.
3a. Therefore, an infinitely old universe cannot exist.
Wes Morriston, Graham Oppy, and others have made objections to this argument. What I would like to do is simply form an cogent inductive argument that would reach the same conclusion as Craig's.
1b. Of the things we observe that have an end, they also have a beginning.
2b. The universe's latest moment of time (the present) is the end of a collection of temporal moments.
3b. Therefore, it is probably the case that the universe had a beginning.
In support of (1b), we might simply provide some illustrations. If I say to a friend, "I finished my term paper," and he responds, "Great! When did you start on it?," I wouldn't reasonably be able to say that I never started it! "I finished it, but I never started it," would be an unacceptable answer to his question. We could give innumerable examples of this. "I just finished counting the number of seashells on the beach," would likewise require that I began to count the number of seashells.
Why, then, would we make an exception for the universe? All of the inductive evidence points to its having a beginning, and this need not include the various scientific data. We can simply use the various illustrations that we experience in which things that end also have beginnings.
(2b) should be fairly obvious. The present moment of time is the last in the series of moments of time that preceded it. So, to make an exception for the universe without some highly compelling reason to do so would result in special pleading. Hence, we have yet another argument for the universe's beginning that may supplement the currently existing arguments. Although not a valid deductive argument, it is in my estimation a cogent inductive argument to the best explanation.
Given the truth of both original premises - (1) and (2), it logically and inescapably follows that the universe has a cause.