At least two of the original 13 states had "official" state-sponsored religions. Maryland was Catholic; I forget what bent Virginia took. Before he died, Jefferson led the fight to abolish the "official" Virginia religion. I forget when Maryland abandoned Catholicism.

Amendment I

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.

"One nation, under God" might be construed to violate the "make no law respecting an establishment of religion" clause, as might "In God we Trust" on our currency. But it does strike me as odd that the courts have gradually converted this into a "no state, no federal agency, no nobody can even mention God anywhere". Naturally Congress itself ignores it, having prayer starting its sessions and including it in the oath of office.