I'm a Christian who believes in the Bible. And I've got a couple dozen books on the Constitutional Convention of 1787 and the Framers of the Constitution in my library. I happen to think that the US Constitution is the finest model of government that man has created. Every American citizen should read a book about that Convention in 1787 (or at least read the Constitution, which I suspect most people haven't bothered to to do). The two books pictured here are excellent. And 'miracle' in the title of this one refers to the unlikelihood of what the Framers accomplished. It's not a religious look at the Convention.
Moving on to the point of this post: The US Constitution does NOT establish the separation of church and state. Read the Establishment and the Free Exercise Clauses of the First Amendment. Heck, I'll type them for you:
Establishment Clause: "Congress shall make no law respecting an establishment of religion..."
Free Exercise Clause - "...or prohibiting the free exercise thereof..."
There you have the actual words written into the Constitution. Separation of church and state is a phrase coined by Thomas Jefferson and used in his letters. The incorporation of that phrase into Constitutional Law has been made by the US SUPREME COURT.
When Congress declares a religion for the United States; or doesn't allow someone to practice their religion of choice, then the government will be violating the US Constitution regarding religion. This public perception that the Constitution establishes a wall between the government and religion is, quite simply, ignorance of the actual Constitution.
If you want to argue that it's the Supreme Court's responsibility to interpret the Constitution and that the Court has decreed that there shall be a separation of church and state, fire away.
But Americans have been misrepresenting and misinterpreting the Constitution up to this day, including saying that it establishes the separation of church and state. No, it does not. It's written right there on the page. Or rather; it's not.