Ahem.
Let me repeat the most salient part.
The U.S. Constitution does not assume a god or rights derived from a god. It is an entirely secular document, a social contract worthy of Thomas Paine. The Constitution is a mutal agreement of the people, it does not make reference to god, derive rights, laws, or authoirty from god. It is a document in which the nation to be built is build on the best intentions and best efforts of the people. You might perhaps be thinking, erroneously, of the Declaration of Independence, which make reference to a creator, in the minimalist, deistic sense - which was as minimal a god as could be agreed on at the time.
That document, however, is not in any sense the legal foundation for the government of the United States. It was a diplomatic screed.
Your premise is false, therefore your conclusion is false.