Who wrote the US Constitution? What sort of men? This is not a question pertaining to character, but to vocation.
The answer is, for a great many of them, "attorneys." A majority of the delegates to the Constitutional Convention were lawyers. Virtually all of them had been active in their state legislatures. Quite a few had served in the Continental Congress as well.
This means that these men were grounded in the traditions of law, the language of law, the patterns of thinking of law, and the experience of law. As such, they constructed a legal -- not moral, not philosophical -- framework for a working republic.
The Constitution of the United States of America is a
legal document. It is not a manifesto -- that function was already served by the Declaration of Independence.
As befits a legal document, the use of language is deliberate. For the most part, this means it is also precise. However, where it is not precise -- the use of the word "slavery" is very carefully avoided -- that, too, is deliberate.
Let's review: In 1787, a bunch of (mostly) lawyers gathered in Philadelphia to draft a legal document. Whatever their misgivings about the end result -- and virtually all of them had some -- they knew that this document would be binding upon future generations. They did not create a government expecting it to last only a few years - particularly when the previous government proved unworkable after just a few years.
If the Founders thought their faith -- Christian or otherwise -- should be an integral part of the fabric of government, they had ample opportunity to say so. Instead, with clarity and precision, they said precisely the opposite!
Moreover, they said it twice. The first instance is in Article VI of the Constitution: "no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States." The second, of course, is the First Amendment. Far from asserting this to be a "Christian nation," they insist that religion is beyond the purview of government altogether.
This does not include the subsequent private declarations by the individual Founders on the importance of separating church and state. There is no need to even bring those up. You're not going to get anything clearer than: "Congress shall make no law respecting an establishment of religion."
It would be nice if those who so loudly proclaim their love of country loved it enough to learn the truth about it. The reality, the history, the facts, are much more inspiring than their slanted rhetoric and sloganeering.