Jamie isn't the son of God - Celine's child is.
The apparent proof of Jamie's divinity comes in the final episode, where he parts a river to allow him and his family to cross. But initially, his demands for the river to get out of his way don't work. It's only when Celine starts praying that it complies. When you consider the fact that Celine is pregnant despite doctors telling her it was impossible, and that God spoke to her in the previous episode, it seems likely that her child is really the second coming of Jesus. Alternately, Jamie isn't the son, but the grandson of God.
The real son of God is Jude. This doesn't necessarily mean he is the Second Coming of Christ (which would make his refusal to pose as the Messiah for the Church depressingly ironic), but he and every one of his progeny has evidence of being at least a little divine:- Jamie: His mother claims he is the son of God. He successfully parts the Thames, and although he does not make it to the bunker, his miracle ensured that Frankie and Celine would survive.
- Ariel: He's the twin brother of the miracle-worker, and by pretending to be Jamie, he presents himself as a false prophet. He could very well be The Antichrist.
- Frankie: A sect of people briefly believed she was the Messiah. Even though this is debunked, she did rise from the dead and is strongly implied to be communicating with and relaying messages from God, or at the very least an angel.
- Celine's child: See the above WMG
