When and how did the idea of a "class-less" society originate in the United States?

I agree with the New World statement, classes are something inherited from kingships, Like the nobility is the highest class. In America you can lose you class status in one generation (kids run the bussiness into the ground).

Gordon Wood's The Radicalism of the American Revolution contains a long discussion of this concept. (personal opinion, the discussion extends longer than useful, and seems focused on responding to an argument that isn't in the book).

I believe the question is founded on (one or more) false assumption; "The United States is a class-less society" is a conclusion, not a pre-existing idea. (others have discussed ad nauseum the imprecision involved in "class-less"). During the 1740's to 1780's, the institution of "class" was dysfunctional in the united states. (Here, I reject the marxist definition as lacking in utility; I refer to the more contemporary notion of gentry class vs commoner). The things that made that institution work in Britain (including the presence and active intervention of a King, a populist Tory party, and a strongly established Church of England) were absent in America.

One could argue that classlessness is an artifact of Republicanism of the period, but even Republicanism was fundamentally oligarchic. (one of the reasons for the failure of the Articles of Confederation was the "licentiousness" of the American populace. Writers of the period lamented the notion that craftsmen and tradesmen and merchants were involving themselves in politics, which was unacceptable). But Republicanism within the British constitution (such as it was at the time) was different from Republicanism in the Netherlands or in Switzerland - I think the argument very quickly drowns under the difficulty of defining Republicanism and Classlessness.

Even if somebody can rise to height, does not make a society classless. Class is not an sealed set of people: people always can move from one class to another. You possibly confuse class with a social estate or caste the two being more closed divisions of society without easy ways to change.

What distinguishes class (by Marx) is the possession of the means of production. That means if a society has those who possesses means of production and those who do not, the society is not classless.

Income also is not a distinguishing criterion: a hired manager can have higher income than a farmer, but still he belongs to a different class.

Not sure I understand well this question: Jefferson writes in the Declaration of Independence:

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.

"The answer is staring you in the face."

Why is the founding document of the United States, often memorized by school children, traditionally read in public on Independence Day, not sufficient to answer this question? It is the document upon which everything rests.

By law, a Constitutional Convention can be convened and a new constitution of the USA can be drafted and ratified. But the United States as a nation remains, as per our Declaration, and therein is stated quite clearly the idea of a "classless society".

(There is much more here - but alas, I have not the time to elaborate at the moment or cite some of the original sources. Perhaps in time - see the wiki on the Declaration for a starting point.)

The last "class" concept I can think of the U.S. having would be segregation. I believe it was the "everyone is equal" movement (The whole "sitting at the front of the bus" thing) that lead to our current class-less "everyone is equal" state.