Washington was a beacon, Jefferson wrote the poetry, Hamilton wrote the prose. So many others.
But how did the USA become what it became? Who or whom came up with this experiment and how? Broad question, I lately realize.
This is quite a complicated question.
The simple answer, following the logic of Bernard Bailyn, is that the Americans modeled themselves after a myriad of principles in the 18th century that lead up to the eventual civil war (or, revolution). Everything below can be found in his book "The Ideological Origins of the American Revolution".
Firstly, we have the enlightenment. In dozens of pamphlets, treatises, etc. from people like Hamilton, Jefferson, and others, there is unending mention of John Locke especially; in fact, he was quoted so liberally he could justify any type of argument American colonists seemed to be pushing. Voltaire, Rousseau, Montesquieu were also mentioned. However, despite this, the brilliance of the enlightenment did not have the greatest impact yet.
Secondly, there is religion. The first "pilgrims", perhaps more accurately religious emigrants, were escaping the religions of Europe to plant the seed of puritanism in the colonies. Yet, by the end of the 18th century, a myriad of religions was taking root, including Anglicanism, one of the religions many sought to rid themselves of. In any case, the various discourses found within religion happily found use in the dialogue of Americans. Even Deism managed to find a way in American dialogue.
Thirdly, we have the English Civil Wars (also known as a revolution) and English thinkers of the 17th and early 18th century as a whole (as well as common law). There is a lot that could be said on it, but Bailyn sums it up well
"The colonists identified with these seventeenth century heroes of liberty: but they felt closer to the early eighteenth century writers who modified and enlarged their earlier body of ideas, fused it in whole with other, contemporary strains of thought, and, above all, applied it to the problems of the eighteenth century English politics".
English liberalism played a major role, probably the largest, in determining the "experiment" that would become America. There are also elements of the classics (of which only Jefferson was perhaps the most knowledgeable on); Aristotle, Socrates, etc., much like English figures of liberty and Enlightenment figures as a whole, saw frequent citation.
I highly recommend his book because he has much more to say than I can in a couple of paragraphs. If you're interested in the topic, of course.