The designers of the US Government specifically granted freedom of religion, forbade religious tests for elected office, and promoted religion and education as good for the nation (see the details in the Northwest Ordinance of 1787, for example). These men lived across a spectrum of religious practice themselves.
Their personal letters and public writing speak to their consistent views about the importance of morality. John Adams famously wrote “Our Constitution was made only for a moral and religious People.” He wrote this in a short letter to the officers of the Massachusetts Militia in October 1798 while he was president. He included these sentences as he commended their work as responsible citizens:
“Because We have no Government armed with Power capable of contending with human Passions unbridled by <, Start deletion,[. . .], End,> morality and Religion. Avarice, Ambition <, Start deletion,and, End,> Revenge or Galantry, would break the strongest Cords of our Constitution as a Whale goes through a Net. Our Constitution was made only for a moral and religious People. It is wholly inadequate to the government of any other.”
The key idea (which is more crucial than “Is the United States a Christian nation?” discussions) is this: Continued liberty under government by the people requires a population of individuals who have self-control, care for themselves, and care for others. Only moral and religious people can do that. You don’t have to be specifically religious but you must be moral. Amoral and irreligious people are far too selfish and greedy to sustain a structure of liberty. History provides multiple examples of these individuals bringing down even great empires.