Either that, or it was so taken for granted that church, faith, God, and all of that were such a part of people's lives that it didn't even need to be mentioned.
It is possible (and I would say, likely) that many of the Founding Fathers of the U.S. did assume that religion was a normal and necessary part of peoples' lives, but that a Separation of Church and State was needed to protect minority faiths and prevent conflict. Religion was no longer the cause of wars in Europe, but it had been recently enough to concern them.
You can also make a good argument that some of the founders were deists, agnostics or even atheists who considered organised religion to be an irrational basis for government policy. Certainly Jefferson seemed to have some interesting views on Christianity given that he re-wrote the New Testament to exclude the Resurrection.
Regardless, the involvement of religion in politics is a fairly recent thing in the U.S. The 'Christian Right' was largely apolitical until it was drafted by the Republican Party in the 1970s and 1980s, and it was driven to do so in a large part as a reaction to the counterculture of the 1960s. Certainly the U.S. was not founded on any religious values - very few nations have been, even those with established religions.