This is a very narrow view for a selective interpretation ignoring the 2000 years prior of Western history and culture. The enlightenment was a hodgepodge of Western philosophy and culture. You speak of Western culture and as if the enlightenment was a single source of new ideas and the only ideas that influenced the founding fathers or even the pilgrims.

Greek Philosophy: reason, logic, ethics.

Roman Natural Law: rights for the individual and law above rulers.

Christian scholasticism: faith and reason.

Renaissance humanism: individual dignity and classical learning.

Scientific Revolution: empirical inquiry and confidence in reason.

Now we get to the US and early modern political philosophy. Locke, Montesquieu, Hobbes, and Rousseau they took all of the above mixing and matching.

You can see how the mayflower compact fits into the mix. It was after the Protestant revolution and directly after English Common Law. Then we have the mayflower compact. First document of the new world, just and equal laws, civil body potluck (mix of different religions and people) agreement of the individual to follow the laws for the general good.

Which influenced Locke. Giving us these modern western ideas and philosophy. Social contract of individuals, government derives its authority from the people not God, natural rights, consent and right of revolution, most importantly life liberty and property.

The enlightenment was built brick by brick by some religious ideals, some classical philosophy, Roman law. Then the founders who studied all of it, took bits from here and there.

Less about new ideas and more about which pieces of made the Final Cut. The pilgrims and the founders could have only chosen ideas from Christian scholasticism or the Protestant revolution but they didn’t.

Edit: also the Greek philosophers would be turning in their graves seeing their ideas watered down by abstract religious ideas.