The universe exists and has either existed infinitely or finitely.
An infinitely existing universe would have run out of energy by now (due to heat death). We know that the total amount of energy and matter that exists in the universe has remained constant since the big bang (we know this due to background radiation that is everywhere in the universe because of the big bang, if energy were leaking into the universe, the background radiation temperature would be higher then it is known to be, slightly above absolute zero). Energy and matter cannot be created or destroyed entirely, only changed in form. So the universe must have began a finite time ago. If we can compare the universe to a clock, the fact that it is running down leads to the conclusion that it must have been fully wound up at some point.
Now that we know that the universe has a beginning, what is it that started it? Here we have two different theories: that the universe was created, or that the universe simply came to be out of matter that had existed in a steady state, the cosmic egg.
Right away we run into problems with the cosmic egg. Why exactly did it stop being a point smaller then an atom and started expanding extremely rapidly? For all things that happen there must be a cause. For an acid to release hydronium it must make contact with water and dissolve. When we find a huge crater in the ground where a city used to be we don't say, "Well, that just happened, there is no cause.", we look for what caused these events to happen. You could say that the egg cracked due to entropy, the natural tendency for all things in the universe to move from states of organization to randomness, it is the increasing randomness of the universe that causes heat death. But this ignores something fundamental to understanding the universes beginning, that there were no laws before the big bang. All physical laws that we know today were created along with it. It is actually not possible to explain the big bang using physical laws because those laws were created by the big bang.
The only option left is creation, but what of the creator? Obviously we cannot know all there is to know about the creator but we can infer a few things. Because the creation of the universe was a creative act, we can conclude that it was produced by a mind. As the universe comprises the totality of nature, containing everything in it that is natural, the creator is necessarily outside nature. As the creator used no natural laws or forces to create the universe, the creator is naturally supernatural. As space and time are within the universe the creator is outside of space and time, which is to say, eternal. As the universe is material, the creator is immaterial, spiritual. As the creator made all matter and energy, the creator must be incredibly powerful, as far as we can tell, omnipotent.
I could go on but I'll leave it at that for now.