The U.S. Government is not secular:
Secular: Not connected with religious or spiritual matters.
Cotting v. Godard, in 1901, the Supreme Court makes the case that the Constitution is but the “body and the letter” of the “thought and spirit” of the Declaration’s founding principles:
The first official action of this nation declared the foundation of government in these words: ‘We hold these truths to be self evident, that all men are created equal, that they are endowed by their Creator with certain unalienable rights, that among these are life, liberty, and the pursuit of happiness.’ While such declaration of principles may not have the force of organic law, or be made the basis of judicial decision as to the limits of right and duty, and while in all cases reference must be had to the organic law of the nation for such limits, yet the latter is but the body and the letter of which the former is the thought and the spirit, and it is always safe to read the letter of the Constitution in the spirit of the Declaration of Independence. No duty rests more imperatively upon the courts than the enforcement of those constitutional provisions intended to secure that equality of rights which is the foundation of free government.https://constitutioncenter.org/blog/republic-found-the-relationship-between-the-declaration-and-constitution