The Founders certainly had personal beliefs, but they were thoughtful about not imposing them on others.
Go, thou, and do likewise.
There is not a single mention in the Constitution about any god or about Christ. Art VI says atheists, pagans, etc. are equal because there "shall be no religious test."
As another poster showed, the Declaration of Independence, among many other writings of the Founders, is loaded with theistic language.
There were very few avowed atheists at the time the Constitution was drafted. The article you cite, indeed the entire Constitution, makes absolutely no mention of atheists or pagans. The intent was to see that membership in any particular sect was not required for office, because there were many sects in America at the time, almost all of them Christian.
Your reasoning is exactly that of the liberals who find imaginary justifications for abortion, property seizures, unconstitutional governmental programs, etc.: You read in things which are not actually in the text.