The Christian tradition has sought to answer the question of its veracity. Certainly, everyone would agree that the Christian tradition has had an impact on the world.
The conflict over myth and history has been a battle in the scholarly world. Was Jesus a historical person, or was he a mythological story. Or was his life a real life mythologized by the Church Fathers?
Myth has been known to be useful to represent things that are beyond the discipline of scienctific exploration. And ancient myths have been useful for eons for religions to build their stories, that help to identify a people and form communities of faith.
The same has happened in America's Founding, I think. Our Founding Fathers used myth to help bring unity, identification to a "people", a diverse people. And the unity was based upon natural law, where all were created equal with certain inalienable rights. So, our unity was in our diversity, not our uniformity. Even the Founding Fathers were different in their religious convictions and commitments. And so should Americans be.
If one accepts the former hypothesis, then, the question becomes, is there a God or not? Does it matter?