But that's a problem for you, why? because it doesn't matter what you believe, the DOI says much differently. As Americans our formulation as free individuals directly indicates "Man" can not "formulate" nor be able to give "those" rights, only a creator. That was the idea which constitutes the whole notion of individual freedom. Without this, there is no America.
Now with that said, you as Atheist are not trying to avert the concept so you are not an enemy of the idea, however there's no way you can live by it. Atheist could not have formed America as it was conceptualized, because if you believe "MAN" gives or formulates rights, then you actually believe in the antithesis of the idea.
Others have tried man giving rights, it never works, and it's called, Totalitarianism.
I can't prevent you from thinking such a ridiculous idea. If it makes you feel good, please, go right ahead--it doesn't affect me one way or the other. Have a good one.