I am a Christian, but many of the Founding Fathers were not. They did come to believe God existed through nature and not the Bible including the New Testament. Many rejected the Bible as the words of men (I do not).
Deism believed in the existence of a supreme being, specifically of a creator who does not intervene in the universe. They believed in studying the natural order of the universe, that man could determine universal truths. The three truths they entombed in the Declaration of Independence was that the Creator had given humans the right to life, liberty and the pursuit of happiness.
Not all agreed as the institution of slavery took almost one hundred years to end after those words were written down. But the abolitionist movement was grounded in this belief that God created humans with the right to be free and that was evidenced by their desire to be free.
Another misunderstood part of history is that people labeled as atheists were what we today refer to as atheists. Instead, an atheist was someone who did not believe in any "accepted" religion. Many "atheists" philosophers of the time did in fact believe in God but rejected every recognized organized religion.
My point is simply, people that believe our nation was intended to be a "secular" nation or ignore the existence of God based on the concept of "separation of Church and state" are wrong. They intentionally mislead others or have not bothered to study the history of our Founding Fathers.
From the beginning our nation was intended to be a Godly nation. There is room to argue what that means, but the Declaration of Independence and the rights of others at the time provide some clarity on this topic.