However, the founders carefully avoided establishing a connection between religion and state.
Religion is manmade; God is not.
God put in man the desire to know and love Him. This is why man is naturally religious. Does it make religion as a whole man-made?
What the Founders avoided is a state religion. Connection between state and religion is obvious from the above. Very clearly, it existed. In fact, it exists whether someone had put it in a constitution or not.