No, and particularly not at the founding of the United States.

It's important to note that our notions of "right" and "left" in regard to politics have evolved dramatically over the past two and a third centuries. Furthermore, those terms tend to be vague and difficult to define, particularly when attempting comparisons across international boundaries.

We get the right-left terminology from the French National Assembly of 1789. During the assembly, most of the representatives of the First and Second Estates (the aristocracy and clergy, respectively) sat on the right of the assembly. Members of the Third Estate, representing the common people, tended to sit on the left.

As J.S. McClelland writes in The Reactionary Right: The French Revolution, Charles Maurras and the Action Francaise, the French right "attacked rationality, universality, and democracy, and in doing so worked out an opposing position of great coherence and force."

I'd also encourage anyone interested in this period to read Michael Fitzsimmons' The Night the Old Regime Ended: August 4, 1789 and the French Revolution, which goes beyond the simple "right-left" trope, which is much more complicated than I'm saying here.

In any event, classical the classical right-left divide was about where the power in government should rest. Should it rest with an elite minority, an aristocracy or senate, or should it devolve to the people, as in a democracy? The United States, with its republic, was much more classically liberal (and thus leftist) in its form of government, than any government in Western Europe when the United States was created.

The United States would soon be surpassed by revolutionary France and other states during the Napoleonic period, and it would also struggle with the limits of how much power should devolve to the people. For example, direct election of delegates to the U.S. Senate was not a part of the U.S. Constitution until the early 20th century. Before then, states could have their legislatures select their Senators in order to insulate that office from public opinion.

If we look to the past using the Right-Left red-blue mentality we have today, we can judge past figures and groups according to our own standards. We need to be careful not to pretend they'd have imagined their own circumstances within these categories. But that said, we can take issues important today and search those issues out in the past. One theme to examine would be race relations. In the mid Nineteenth-Century, the US was practicing Black slavery and pursuing Manifest Destiny against Mexican and American Indian peoples. Europeans were building and consolidating their empires. But Britain and France banned slavery in their colonies during this century. And abolition had not required any revolution (with the obvious exception of Saint-Domingue/Haiti). So in a sense, Western Europe appeared to be more progressive on this issue. Then you look at the behavior and attitudes of the British and the French during the US Civil War - James McPherson tells us in his book about Antietam that both governments were considering recognizing the Confederacy and possibly supporting its cause for independence. Were that to have occurred, the Civil War could have ended much differently. Racialized slavery could very well still exist with a fragmented US serving in some kind of unequal neo-imperial relationship with those Western Europeans. Obviously this is conjecture, but contemplating contingency is still a worthwhile and well-valued historical exercise. My favorite text illustrating this unfortunate heritage of social democracy in Western Europe is WG Sebald's Rings of Saturn where he runs into some ancient Belgian pensioner and thinks about how Congolese suffering made her comfort in old age possible.

So one of the ways that the US is significantly "right" of European countries is with regards to the welfare state. Why the US welfare state is so different from that of other Western democracies is a long-standing preoccupation of some political scientists. One of the explanations I found most interesting is that in the US the franchise was expanded (to white males regardless of property ownership) before the development of an administrative bureaucracy. This led straight to the spoils system, where people were rewarded for their support of political parties with positions in the civil service. This created an association between government power and corruption. When reforms came later, they sought to restrict administrative autonomy. In many European countries, however, the bureaucracy developed before the franchise was extended, and after the franchise was extended, the new voters tried to gain access to the bureaucracy and its services rather than curb its influence, which meant expanding the welfare state.

I don't think this theory can explain everything, but it's interesting, and it ties the classical notions of right and left (the aristocracy vs. the common people) to a more modern one (expanding vs. constricting the welfare state), suggesting that the US is more "right-wing" now because it was more "left-wing" in the past.