If the framers and/or the first Congress ever wanted to make it clear that they intended to divorce religion entirely from government, they could have quite easily left a manifest testimony to that effect by abolishing military chaplains. But, of course, they didn't. Surprise, surprise.
Military chaplains on the North American continent pre- and post- date the Constitution. And, to this day, they are still here. Like Congressional chaplains, their salaries are paid by public money. The same can be said of prison chaplains.
It is important to note that the passage of the First Amendment in no way vanquished the office of military chaplains. Indeed, like Congressional chaplains, they fulfill a spiritual office within the public realm. There is no indication that the office of military chaplains violates the establishment clause.
The first Congress, if they wanted to completely separate church and
state, could have made a case that military chaplains are a violation of
that principle and dispensed with them. But such was not to be. They exist
from then to now, serving God and country, quite literally.