Well the people who founded along with the vast majority of the people who lived here had a belief in a deity, most were Christians of one denomination or another.
The belief was the basis of the Natural Law as embedded in the Declaration of Independence, 'men are endowed by their Creator with certain inalienable rights' (hope I got the quote correct).
This was a critical feature of our republic, since one got their rights from God then the government couldn't take them away, and if they tried you have the right to revolt and overthrow said government. IOW in America people give powers to government, government does not give rights to people.
In most other political system the government 'grants' rights to the governed and of course can take those rights away, the road to tyranny is already paved.
No God, No Faith, No Inalienable rights, no freedom.