Um...
Noooo....
THe US constitution does not mention God once.
It does mention religion, Twice.
In Article 6 is say that no religious test shall ever be allowed for holding any office within government.
This very carefully ensures that the government CAN NOT consider any religious belief, nor lack of religious belief, in hiring or electing government officials.
Secondly... there is the first amendment which forbids the government from ANY action that might favor any religion....
Which mean no money going to them, no law endorsing any religious practice,, no favoritism can be shown to any religion.
The Phrase "separation of Church and State" was used frequently by Adams, Jefferson, and Madison in describing the specific intent of the constitution's construction.
So, you're wrong. The men who WROTE the constitution made quite clear exactly what the founding fathers intended the document to do--- which was to create a SECULAR state.
Adams wrote that history shall never state that we were driven by any divine inspiration...but rather created this government entirely as the result of reason...
Adams and Washington, in fact, in treaty negotiations with Tripoli stated quite clearly that the United States was NOT, never has been, and never shall be a 'christian nation'.
Therefore... the people who wrote the document, who crafted this nation, were quite clear as to their intentions. They wanted this government to be the first in history totally unaffiliated with any faith.
And as to the phrase not being in the constitution...
Next time you run a red light why don't you try telling the judge that the light did not say the word "stop".
Your statement is about that ridiculous.