"To answer the question, why I believe God exists, the most concise way I can say it is that the alternative is so absurdly problematic. That is, without a transcendent cause we have to accept the notion that everything we know to exist either came into existence out of nothing, or that it is past eternal (see Hilbert's Hotel and the problem of an actual infinite). Both of those propositions to me seem much more unlikely than the existence of God."

This problem just requires a cause for the universe. But that cause doesn't necessarily need to be a conscious being that listens to prayers and still has control over everything.

"The second answer would be the appearance of fine tuning of the fundamental constansts of the universe for intelligent life, without which our existence would be impossible. Again, without a God I have no cchoice but to believe that this appearance of fine tuning is nothing more than an accident. Technically possible, but still requiring much more of a mental stretch than the belief that something, or someone created it."

It's happened over a very long period of time. As I understand it, random mutations happen, and those that aren't a hindrance to survival tend to get eliminated. When people can't accept this as an explanation, it's because they are failing to grasp the huge timescale over which it happened.

"Well, if we think about the kind of being that would have to exist in order to create the universe, and set it up for intelligent/sentient life...we would need something that is enormously powerful, transcendant of time/space, immaterial, and unfathomably intelligent. Sounds an awful lot like the traditonal conception of God to me."

But the universe was not created the way it currently is. The universe immediately after its creation would have been totally unrecognisable compared to the universe of today.

"The only question remaining is whether or not God is the ruler of the universe...and for that we also have an unlikely alternative: that a being as unfathomably intelligent, and powerful as he must be has no interest in how his creation ultimately ends up, and/or no power to influence it."

But look at how things have turned out. This is not the creation of an all-powerful being that cares. If an all-powerful being created this, they didn't care about it turning out well. And no, human free will does not account for all the bad things in the world. Many bad things are not created by humans at all. But even if they were, if an all-powerful being created us, he knew it was going to turn out like this. What kind of maniac creates an imperfect species and then punishes them for the flaws he created in them? That is literally like a parent bringing their child up badly and then blaming that child for all the things they then do wrong.