Your point about the Constitution not including reference to God is not good logic. Yes, God is not mentioned. However, it is the document establishing the rules for the government. While I certainly agree that it is curious to not even have anything in the preamble of the Constitution, the Declaration of Independence is what explained our philosophy of government. That is why God is mentioned there, while the Costitutition, which dealt with the nuts and bolts of how things would run, did not.Remember that the Constitution was not even the first founding document. The Articles of Confederation were. They were scrapped and replaced by the Constitution.
The Declaration was principly an explanation of why we felt the need to revolt against British rule. It was not meant to establish the governing philosophy of the nation any more than Common Sense was. That was done first by the Articles and later by the Constitution.
It's not merely curious that the Preamble contained no reference to a deity. There is every reason to believe that it was quite intentional. Madison, while a Christian himself, was a firm believer in Separation.
-Eric