A thought experiment meant to show that God does not exist left me with a different reaction: the argument may work against a particular picture of God, but not against the one I hold. The more I read, the clearer it became that many people are using the word God to mean something quite different from what I mean. I am a theist, and what follows is simply my own understanding.
Many religions present God in concrete, person-like terms. In the Bible, for example, God is supreme, all-knowing, all-powerful, yet also capable of pleasure and anger. That kind of portrait looks very human. I do not think of God that way.
For me, God has no physical form, or at least cannot be observed as an object. God is not a being among beings, not a figure produced by imagination. God is everywhere, present in everything in the universe and also in each of us. The personified God of Christianity is, in my view, a human attempt to observe and describe God. It is not an accurate or complete account. It carries misunderstandings and biases.
God is the whole of all things, material and spiritual. God is truth, a higher-dimensional existence. Even science, as the body of knowledge humans have explored so far, is only a part of God. God exists before the universe and continues infinitely backward and forward. God is enduring and permanent. The rules, laws, and evolution of the universe all fall within God's scope. God can be what people call Heaven, the truth we seek, or the ultimate mystery science wants to reach. Religion, philosophy, and science are all partial means of knowing God, and each has its own limits.
If the Bible was written by multiple people under divine inspiration, it still passed through human hands, human language, later changes in context, translation problems, and the need to fit particular times and environments. By current cultural standards, it is not accurate. So I do not tend to read the Bible as truth itself. It is one tool among others for approaching God.
Good and evil are human subjective judgments based on our own moral standards. God does not have good and evil in that human sense. God operates by a rule that is cosmic law and truth. God does not need to be judged, because God is the supreme existence with absolute power—power, not a right. God is the universe and all things. When people say God is good and merciful, they are describing God's actions as absolutely correct, not measuring God by human preference.
Human thinking, culture, science, and technology are limited, so different religions understand God differently. That is why different traditions and factions have different gods. Every one of those understandings is somewhat off.
I strongly dislike the habit of placing theism and science on opposite sides. I am especially uncomfortable when creationism is used to attack Darwinian evolution. Such conflicts usually come from half-understanding either theism or evolution. The bad argument is a result of insufficient knowledge, not a real incompatibility.
Science is built from human empirical knowledge. Within a theistic framework, science can perfectly well be one way humans explore and understand God.
Suppose evolution were absolutely correct—only a supposition, since no one should claim absolute certainty. We could understand evolution as one of the rules God established for this universe. The evolution of living things would also be attributed to God. Science focuses on facts, phenomena, results, and reasonable inference. It cannot determine what is invisible or imperceptible to it. God is there.
Take the speed of light in vacuum: 3×10^8 m/s. Why exactly that value? Why not faster or slower? I have not seen science give a satisfying answer. If the question is forever unsolvable, theism can say God set it at that value. Perhaps in some other world God set another speed, say 4×10^8 m/s.
Take probability. We toss a coin. Is the first toss heads? We only know the probability is one half. But if the first toss really is heads, why is it heads? If the second is heads too, why is the second heads? We seem unable to answer. Theism can say probability is one of the laws God created for the universe. God can make the first toss heads and the second toss heads without violating the probability law God established. Perhaps in another parallel universe God created a different probability theory: the chance of heads is 100 percent, no matter how the coin is tossed. People in that universe would also think their theory is correct, because it matches their experiments.
So I believe God exists. God is unique, but also infinite, supreme, and omnipresent. God is not good or just in the subjective human sense. God is omniscient and omnipotent, because everything in the world is God's own creation, and the world does not escape God's control.