[Psa 19:1-4 ESV] 1 To the choirmaster. A Psalm of David. The heavens declare the glory of God, and the sky above proclaims his handiwork. 2 Day to day pours out speech, and night to night reveals knowledge. 3 There is no speech, nor are there words, whose voice is not heard. 4 Their voice goes out through all the earth, and their words to the end of the world. In them he has set a tent for the sun,

[Rom 1:18-22 ESV] 18 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who by their unrighteousness suppress the truth. 19 For what can be known about God is plain to them, because God has shown it to them. 20 For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. 21 For although they knew God, they did not honor him as God or give thanks to him, but they became futile in their thinking, and their foolish hearts were darkened. 22 Claiming to be wise, they became fools,

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.

just because something is written down does not make it true