Premise 1
Actually, I didn't say everything needs a cause, I said everything needs an explanation of its existence. As I wrote earlier in the post: "These things have explanations of their existences, either in self-existence or by an external cause." If a thing is self-existant, it exists of its own necessity, and must be eternal. God is like that. I also leave open the possibility that abstract objects like numbers are self-existant, although I conclude that they, though eternal, are also contingent on God.

"What caused God?" you say. This is a really bad argument and atheists should stop using it. As I said, everything needs an explanation, not a cause. God's explanation would be self-existence. Abstract objects could be self-existent, or they could be contingent on another source (here, God). Non-eternal things are necessarily externally caused.

I apologize for being imprecise in my wording. Misleading, even. When I said everything must descend from an initial cause, I did not mean to rule out that a thing may be one of those initial causes, and hence not descended from an initial cause. Also, I called them "initial causes" because they perform the action of causing, not because they were caused. Any initial cause must be self-existent.

Here we're seeing how much this argument ressembles Leibniz' Cosmological Argument, since I must essentially resort to it's premises to establish my own.

Your entire objection to Premise 1 was based on a misunderstanding. Furthermore, you asked "What caused God?" as if this question rules out God as a possible initial cause. If so, there can be no initial cause, since you could always say "What caused x?" In any case, we've already seen that the question is mistaken, and that eternal things don't necessarily need a cause, and self-existing things don't have causes.

Premise 2
Your objection to premise 2 is based on your invalid objection to premise 1.

You say that God as an initial cause is not an element of the set of possible explanations. You apparently say this because of that same question, "What caused God?" (which we've debunked) which applies to any element of the set.

I'm not sure about this next point, but I think you were also saying that including God as a possible explanation assumes God's existence. This is an absurd objection—no offense. Obviously, I must assume God is a possibility in order to try to prove his existence.

Premise 3
You think the Big Bang is a better initial cause than God. I heavily object to this.

First of all, I'd throw your own question back at you, "Who caused the Big Bang?" According to your previous reasoning, this removes the Big Bange from the set of possible explanations.

Actually, this question is valid for the Big Bang, since nobody claims that the Big Bang was a self-existing, eternal entity.

Furthermore, I resort to my point about this initial cause having all maximum or minimum values. The qualities of the Big Bang are all a bunch of arbitrary values.

Finally, scientifically, I don't believe in the Big Bang. It has too many problems.

If something had a mind, why did it choose to start causing then and there. As to why a natural event didn't do it earlier? Because there was no earlier. In a natural explanation, time and space did not exist before everything started.

Even with a mind, time & space didn't exist before everything started. So I guess this whole point goes out the window, anyway.

However, by saying something that had a mind started everything, then this object with a mind would exist. What capacity does this entity exist in if nothing existed?

I may need clarification here. Are you saying: "How did it exist without space? How did it exist without time?"? If so, I don't see any reason a metaphysical entity would require time & space to exist.

In the end, my argument, I admit, is a "bad" argument—not in the sense that it's unsound, as you'd say, but in the sense that it's pointless and hard to use. Why use it at all, if it resorts to some of the same points as Leibniz, but uses them less well?

I'll defend it still.