Those who came to America willingly and first, who moved here before there were ports and railroads, came here for the opportunity to worship God as they chose, in freedom. When these wise men wrote the constitution, their intent was to keep any church out of the government, not to keep God out.
They made some mistakes. They did not emancipate either slaves or women despite pleas for both.
Nonetheless they created a document that has served to keep us free and stable while other governments collapsed. For more than 200 years we have been the land of the free and the home of the brave, the land of milk and honey, with enough for everyone willing to work.
Each incoming group in turn was castigated and set apart, the Irish, the Jews, the Germans, the Swedes, the Chinese, the Japanese, the Africans, but they learned the language, they learned to be free, and became Americans. They brought their customs, traditions, morals, and ethics, but they added them to the mix and became Americans.
And all had the same desire. To work, raise a family and worship in freedom. They benefited from the wisdom of those who kept all churches out of the Government but kept God at it's heart. This is what is forgotten. That any government without God at the center will be a government such as we have today.