So glad you chose that example. Thomas Jefferson was a deist, he believed in a god, but thought that that god did not intervene in worldly affairs and that thus spending time worshiping him was a waste of time. He also had the right idea about organized religion, let me give you some more of his quotes
In every country and every age, the priest had been hostile to Liberty.
I do not find in orthodox Christianity one redeeming feature.
I have recently been examining all the known superstitions of the world, and do not find in our particular superstition (Christianity) one redeeming feature. They are all alike founded on fables and mythology.
So yeah, I think he had the right idea about the role of religion, he was also a strong proponent of the separation of church and state, another good idea.
As for god, yes, the declaration of independence does mention it, the constitution does not - can you tell me which of those two is a legal document?
Finally, the founding fathers were great politicians in their day, but the largely were not scientists, we know a lot more now than they did then, and the concept of god is just not necessary. If you want me to believe in your invisible sky-daddy, you're going to have to give me some concrete evidence that the exists, not just point out that others have and do believe in it.