Here's the wikipedia article, references are cited within.
https://en.wikipedia.org/wiki/Moses#Historicity
No, the word god never appears in the constitution.
You have cited the Declaration of Independence, which is not a US legal document (meaning that while it is a historical document, it has no relevance to the modern US legal system). It also predates the constitution's Bill of Rights by 15 years, which established freedom of religion.
Even at that, "creator" does not mean the Christian god. That document was written by Thomas Jefferson, who was a deist and quite aggressively outspoken against Christianity. So even on that count, your argument doesn't hold water.
Regardless, this has nothing to do with policy or passing legislation, Abraham didn't do that sort of thing. God chose Abraham and Abraham accepted on behalf of the ancient Israelites. So, if God chose Barack Obama, and Barack Obama accepted on behalf of all Americans, are you and all of your descendants therefore tied to that vow that you didn't make?