God is a position. It's not a name. I hate how everyone always gets this confused. "God" is not a name. It's a position that some being fills. Christians fuck this up all the time. Under old tradition, Yahweh was too holy of a name to say so people just started saying "god." That's how it evolved basically.
Again, people are confused about America. The pilgrims didn't write the Constitution and they did not make America in anyway. They still considered themselves British at the time. They did indeed leave for religious purposes but this has nothing to do with our Constitution. Go about 150 years later and then you have Deists (not Christians for the most part) making the country and writing the Constitution, etc. You gotta be really careful not to mistake the word "God" with the Christian god. Many time, it very well could have been just the Deist god...not Yahweh.
So don't confuse:
1.) God: the position and the being
2.) the Pilgrims and the Founding Fathers