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The U.S. Constitution is a secular document. It begins, "We the people," and contains no mention of "God" or "Christianity." Its only references to religion are exclusionary, such as, "no religious test shall ever be required as a qualification to any office or public trust" (Art. VI), and "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof" (First Amendment). The presidential oath of office, the only oath detailed in the Constitution, does not contain the phrase "so help me God" or any requirement to swear on a bible (Art. II, Sec. 1, Clause 8).
In 1797 America made a treaty with Tripoli, declaring that "the government of the United States is not, in any sense, founded on the Christian religion." This reassurance to Islam was written under Washington's presidency, and approved by the Senate under John Adams.
We are not governed by the Declaration. Its purpose was to "dissolve the political bands," not to set up a religious nation. Its authority was based on the idea that "governments are instituted among men, deriving their just powers from the consent of the governed," which is contrary to the biblical concept of rule by divine authority. It deals with laws, taxation, representation, war, immigration, and so on, never discussing religion at all. The references to "Nature's God," "Creator," and "Divine Providence" in the Declaration do not endorse Christianity. Thomas Jefferson, its author, was a Deist, opposed to orthodox Christianity and the supernatural.
The words, "under God," did not appear in the Pledge of Allegiance until 1954, when Congress, under McCarthyism, inserted them. Likewise, "In God We Trust" was absent from paper currency before 1956. It appeared on some coins earlier, as did other sundry phrases, such as "Mind Your Business." The original U.S. motto, chosen by John Adams, Benjamin Franklin, and Thomas Jefferson, is E Pluribus Unum ("Of Many, One"), celebrating plurality, not theocracy.