"No people can be bound to acknowledge and adore the invisible hand which conducts the invisible affairs of men more than the people of the United States. Every step by which they have advanced to the character of an independent nation seems to have been distinguished by some token of providential agency.... We ought to be no less persuaded that the propitious smiles of heaven cannot be expected on a nation that disregards the eternal rules of order and right, which heaven itself has ordained." --George Washington
"It is rightly impossible to govern the world without God and the Bible." --George Washington
It is the duty of all nations to acknowledge the providence of Almighty God, to obey His will, to be grateful for His benefits, and humbly to implore His protection and favors." Thanksgiving Proclamation, October 3, 1789
"Statesmen, my dear Sir, may plan and speculate for Liberty, but it is Religion and Morality alone, which can establish the Principles upon which Freedom can securely stand." John Adams, Letter to Zabdiel Adams, June 21, 1776
"We have no government armed with power capable of contending with human passions unbridled by morality and religion...Our Constitution was made only for a moral and religious people. It is wholly inadequate to the government of any other." -John Adams {John Adams, The Works of John Adams, Second President of the United States, Charles Francis Adams, ed. (Boston: Little, Brown, 1854), Vol. IX, p. 401, June 21, 1776.}
"Suppose a nation in some distant region should take the Bible for their only law book, and every member should regulate his conduct by the precepts there contained! Every member would be obliged in conscience to temperance, frugality and industry; to justice, kindness and charity towards his fellow men; and to piety, love and reverence toward Almighty God." --John Adams
"The sacred rights of mankind are not to be rummaged for, among, old parchments, or musty records. They are written, as with a sun beam in the whole volume of human nature, by the hand of the divinity itself; and can never be erased or obscured by mortal power." Alexander Hamilton 1775
Benjamin Rush: "Without the restraints of religion and social worship, men become savages."
I could go on, but you should get the point by now.
America was founded as a non-sectarian Christian country.
I have no doubt that most, if not all, of the Founders were Christians. I also have no doubt that they did not found a Christian nation. There is no single quotation which you have provided, by Washington, Adams, Hamilton or Rush, which states otherwise.
This one comes close:
"It is rightly impossible to govern the world without God and the Bible." --George Washington
However there is no record that Washington ever said it. It's a pity that you have to resort to misquoting Washington to try to make your point.