This is something American Creation has yet to really touch. Hat tip First Things to this article. As it notes, the term was not invented until around the 1950s. President Eisenhower summed it up:
“Our form of government has no sense unless it is founded in a deeply felt religious faith, and I don’t care what it is.”
But as a commenter at First Things noted, George Washington and the other "key Founders" anticipated this concept, citing Washington's letter to the Jews. Yet, Washington also believed Muslims and unconverted Native Americans worshipped the same God Jews and Christians did, suggesting the need for a broader, more inclusive term like "theism" or "Providentialism."