The first of William Lane Craig's arguments for the existence of God is the Kalam Cosmological Argument. It goes:
1. Whatever begins to exist, must have a cause of its existence.
2. The universe began to exist.
3. Therefore, the universe has a cause of its existence.
The first premise of the argument seems intuitive, at least at first. Suppose you and I are eating lunch. You turn your head away from the table, only to discover that a bunny rabbit is munching on your salad. You ask "how did that rabbit get there?" and I say "Funny thing. It just popped into existence. No cause or anything, it just happened." You wouldn't take me seriously, right? Well, what goes for bunny rabbits should go for universes. To say that the universe began without a cause doesn't make sense.
Or does it? Opponents have argued that in Big Bang theory the time begins when the universe begins. So there never was a time before the Big Bang in which time existed but the universe did not.
Somehow, this doesn't in my mind alleviate the need for a cause. It seems to me that something that doesn't exist contingently should have existed through an infinite duration. if it doesn't have a cause, similarly, it should exist through an infinite time, or be outside of time.
But why believe that the universe had a temporal beginning? The most prominent theory in cosmology seems to still be the Big Bang theory, a theory that says that there was a beginning. But Craig also endorses arguments that there can't be an infinite number of past moments.
Think about this. Suppose I ask you to loan me some money. I offer you 100% interest compounded daily. But you, quite rationally, want to know the term of the loan. I reply that even though it may take an infinite length of time to pay it back, you'll get your money. This somehow doesn't satisfy you. But if the past is infinite, that means that there are an infinite number of moments in time that have ALREADY HAPPENED. How is that possible?
I have a link to a presentation of three arguments in favor of the claim that the past must be finite and not infinite.