Here's the First Amendment in the Bill of Rights(Congress, 1789 and ratified 1791):
"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances."
I interpret that to mean that Congress is not to establish a particular religion or prohibit a particular religion. I don't think innocuous statements on currency such as "in God we trust", or "one nation under God" in the pledge of allegiance is violating the first amendment (and obviously the U.S. Supreme Court doesn't either).
It could be argued that atheism and agnosticism is a religion, and that these clauses violate their first amendment by passing a law that establishes a general theist religion, but 'God' is no where defined in the pledge or in currency. Given the wide range of meaning to the term 'God', I can't imagine why this would bother anyone. If we interpreted 'God' as Stephen Hawking does (i.e., equivalent to the laws of physics), then we might mean that we trust in the laws of physics or that we are one nation under the laws of physics. Even if an omniscient God is what is assumed, it is not establishing a religion by endorsing the existence of God, it is endorsing a philosophical view. There are plenty of philosophical views endorsed in the Constitution and Bill of Rights. Heck, even the belief in freedom of religion, speech, etc is a philosophical view about how humans should be governed and what rights they deserve!
I think what you are looking for, more than anything, is an amendment which rules out a particular philosophical view from being endorsed by Congress. This, of course, is not in the Bill of Rights, and Congress is free to endorse particular philosophies as long as they do not violate the Bill of Rights or the Constitution.
Warm regards, Harv