I suppose this is my fault for focus on points raised by others. However, I am going to answer. I am going to say that these are outlines, as the arguments and commentary fill thousands of tomes, and given the current state of the Amarr Empire, they’re all in the back corner gathering dust.
1: The First Mover, or Unmoved Mover. In our world, we see a chain of cause and effect. I do something that causes something. That effect, then causes something else. This for this chain to regress ad infinitum, would be impossible, because in short, logic really starts to break down when the concept of infinity comes into play. However, it’s not less fantastic to believe that there is an infinite causal chain having no beginning than that existence of God, who started this event. So, this argument states that the first cause in this chain had no effect. God stands outside time and our understanding of the world.
2: Similar to the First Mover, is the First Cause. In the world we can see that things are caused. There is a hierarchy of scientific principles that govern the universe. Stars are dependent upon atomic fusion, which is dependent upon gravity, dependent on mass, dependent on the Higgs field and boson. Again, this cannot be an infinite regression, so what ever this principle cause of existence is, whatever this final dependency upon all creation rests, is God.
3: Judgement. We can see in the world things are good and bad (generally.) We can look at a drawing of a circle and judge it to be better or worse than a circle drawn with a compass. We can be sick or healthy. We can look at the Imperials that murder and kill our people and judge them to be less than the ones that do try and help. However, all this implies a standard, that no matter what your criteria is, there is a standard of goodness. And there is something that is goodness itself. This is God.
4: Final Cause. We observe every day non-intelligent objects behaving in regular ways. The hydrogen in starts continues to fuse. However, such things are static. Even the staunchest atheist would not argue that this can be neither do to chance; if it were, then chance would dictate some things just happen. Gravity can be manipulated, but never goes off on its own program. I have never jumped and not come down because gravity decided not to work that moment. These non-intelligent things cannot set themselves. God has set them. The final cause is related to the first cause, in that if a cause and effect chain exists, at a certain point, constants were removed from that chain.
5: Intelligent Design. The world is orderly and predictable. All objects that exhibit such order are the products of intelligent design. Therefore, the universe is the result of an intelligent design. God is the intelligent designer. A more classic statement is that if you were walking on a planet and found a complete Rifter, would you assume that it just came into existence by random chance, or that someone built it? Is the universe less or more complicated than a Rifter?
6: The Greatest One. God is that which nothing greater can be conceived. This idea of God is sound and contains no logical contradictions. That which can be through of as not existing is not as great and that which cannot be though of as not existing: contingent v. necessary. To conceive of a god that possibly doesn’t exist is not to conceive of the greatest being, since the greatest conceivable being could not be nonexistent. Therefore, God exists. This is what happens when monks have a lot of free time, a self contained logical argument. I want to say that this is vastly simplified. Vastly. I would underline that if I could.
Note that all of these arguments simply focus on God’s existence. They do not answer what kind of God He is. Do you want walls of text? This is how you get walls of text.
I even cut this down a lot.