There may not be "proof" in the scientific sense, but we can use reason to see that there has to be a God. St. Thomas Aquinas formulated five ways that we know the existence and necessity of God.
First, the argument from motion. Some things in the universe are in motion. All things that are in motion require a mover. An infinite regress of motion is impossible (in other words, if we say A moved B moved C moved D moved E moved F et cetera, it doesn't make sense to say that that goes on forever. This is simply because if for each individual motion there is a mover, why would the same not be true of all motion looked at together?). So there must be an unmoved mover which moved all things, and this we call God.
Second is the argument from Causality. Some things in the universe are caused. All things that are caused require a cause. An infinite regress of causation is impossible (for the same reason as above). So there must be an uncaused cause which caused all things, and this we call God.
Third is the argument from Contingency. Some things in the universe depend upon others for their existence. We call these contingent beings. It is impossible for all beings to be contingent, since something can't come from nothing. Therefore, there must be an independent being from which all things derive their existence, and this we call God.
Fourth is the argument from Degree. There are varying degrees of perfection in nature (that is, some things are greater beings than others. A rock is completely passive, a plant is somewhat passive, an animal is sensitive, a man is rational and can form judgments of goodness--thus he has the highest knowledge of these things). To speak of degrees requires that we admit of a standard of perfection from which lower degrees derive their perfection. And so there must be a pinnacle of perfection by which we measure the goodness of all things, and this we call God.
Fifth is the argument from End (or purpose). Some things in the universe act toward some purpose, and we call them natural bodies. These natural bodies are themselves to some degree unintelligent, but acting for a purpose is a sign of intelligence. Therefore, there must be a higher intelligence guiding them toward their purposes, and this we call God.
So we can see that the world simply doesn't make any sense without a God of some kind. We can also deduce from all of this that God must be loving: if he caused all things, it had to have been from love. To love is to will the good of another, and since it is better to exist than not to exist, God must love what he has created. Sure, there is pain and suffering in the world, but this is not caused by God. It is caused by man's disobedience against this natural order God has established. Further, God, being all-good, manages to bring good out of suffering. This is most exemplified by his Son's sacrifice on the Cross--the very worst thing that could ever happen, the death of God at the hands of men, became the very best thing that could ever happen: the salvation of all mankind.