The phrasing you reference is not intended to reference a theistic creator, rather as a way to acknowledge that it is not the role of government to confer rights to the people - we are owed them inherently. “Our creator” could just as readily be interpreted to mean a series of entirely natural processes that can be explained by scientific principles.

The founding fathers themselves explicitly acknowledged that the government was not founded on religious principles on many, many occasions. If you need more details on this, the anti-defamation league has compiled several good quotes here: https://www.adl.org/sites/default/files/documents/assets/pdf/civil-rights/religiousfreedom/PORF-StatsFF.pdf

You are free to believe (or not) in anything you like, but there is no place within our government for the consideration of religious beliefs in how we make or apply our laws.