I've no idea how I managed to produce not one, but two children who were advanced analytical thinkers whilst their age was still in single figures. However, I did.
They have both, independently come to the conclusion that there is no god by very different means.
My eldest used deductive reasoning. He'd lost a few teeth, and got the obligatory tooth fairy exchange rate. One tooth, he neglected to tell the tooth fairies representatives, and the money was not forthcoming. When he told us, suddenly there was money. We'd always said if our children asked us the questions "does the tooth fairy/Santa/etc exist?" we would answer honestly.
My son had worked out that as we needed to know that the tooth was there, that it was, in fact, his parents who were the tooth fairy. He asked, we admitted it. This was just before Christmas. While writing his list to Santa Claus, he realised that the list had to pass by Father Christmas's representatives in order for Santa to know what was on his list, and again, he made the connection. He asked, and again, we admitted it.
In both cases, he was under strict instructions not to spoil his brother's belief.
What was remarkable was that he then made the connection between the Tooth Fairy, Father Christmas and God. My wife is Methodist, which is about as close to atheist as you can get whilst still going to a church. I am atheist. Therefore, it was me that he came to and asked the question. Santa and the Tooth Fairy are one thing, God is another. Many adults believe in a god whilst simultaneously disbelieving in Father Christmas and the Tooth Fairy. They find no contradiction here. My son did, and joined me on the enlightened and rational side. It was a little disappointing to my wife, but hey ho.
My youngest son came to the conclusion that God didn't exist from a different direction.
My wife has been taking him to church for a while, and eventually, they got to the bit where God made Man in His own image (and this is why he is always depicted as a culturally specific anthropomorphic personification). This led him to the idea that there must be a god for each type of animal that made those animals in His own image. A god of chameleons, a god of zebras, a god of clown fish, etc. The next leap impressed the hell out of me.
He could not work out what the God of gods would have to look like in order to create the gods that create animals in their own image. My wife explained that God was not created by a god, which confused him more. So he asked me the question. I told him the same as I had my eldest. Some people believe in God, others believe in a different God, and some believe in a large bowl of noodles that controls the universe. I then told him that it wasn't necessary to believe in any of them. This was the path he chose.
He hasn't made the connection to Father Christmas and the Tooth fairy yet, so shush. Mum's the word.