The Wealth of Nations was published in 1776, a year into the Revolutionary War, yet by peace of 1783 copies of the book were already making their way across the Atlantic. Adam Smith did NOT invent the field of Economics and his ideas about free trade were hardly new, they were common among people of the Enlightenment and especially the Founding Fathers. It should be mentioned that Adam Smith actually met Benjamin Franklin in England in the 1760s and the two kept correspondence, some speculate that Franklin even read early drafts of the Wealth of Nations. Jefferson and most of the Founders were more familiar with the French Physiocrats such as Quesnay and especially Turgot who were very anti-mercantilist and interventionist in their own right. Jefferson and the Anti-Federalists took strongly to the Physiocrat idea that true wealth comes from the land, which means farming is a noble profession while banking and commerce should be viewed with suspicion. Alexander Hamilton, because of his background as a merchant and his interest in banking is believed to be the first to read the finished work of the Wealth of Nations, possibly as early as 1781.

There are some Episodes of Historian Clay Jenkinson's award winning podcast the Thomas Jefferson Hour that deal with this topic:

*Show 938, Untrammeled Economy in which the Dr. Jenkins interviews "Adam Smith" as portrayed by Smithian scholar .

*Show 736: Physiocrats

Regarding the idea of redistribution of wealth, it was actually talked about during the Enlightenment, especially among Rousseau but it also appears in the work of John Locke , a philosopher who had an immense amount of influence on the Founding, the Jefferson hour talks about the topic of redistribution in Jeffersonian thought. There is a growing amount of scholarship on the topic of redistribution in currents of Enlightenment thought which you can easily find as well.

Though a constitutional basis for "capitalism" is a popular theory in recent political discourse, there's strong support for the notion that while the Constitution does enshrine the concept of private property in the Fifth Amendment, especially as amended, it does not mandate a strict laissez-faire approach to the marketplace.

Justice Holmes's short dissent in Lochner v. New York, 198 U.S. 45 (1905), is instructive. In that case, New York State passed a law setting maximum hours and other sanitary conditions for bake shops. The Supreme Court found that these limitations impinged on the due process right to contract freely. Holmes would have held otherwise:

This case is decided upon an economic theory which a large part of the country does not entertain. [. . .] The Fourteenth Amendment does not enact Mr. Herbert Spencer's Social Statics. The other day we sustained the Massachusetts vaccination law and state statutes and decisions cutting down the liberty to contract by way of combination are familiar to this court. Two years ago we upheld the prohibition of sales of stock on margins or for future delivery [. . .] The decision sustaining an eight hour law for miners is still recent. Some of these laws embody convictions or prejudices which judges are likely to share. Some may not. But a constitution is not intended to embody a particular economic theory, whether of paternalism and the organic relation of the citizen to the State or of laissez faire. It is made for people of fundamentally differing views, and the accident of our finding certain opinions natural and familiar or novel and even shocking ought not to conclude our judgment upon the question whether statutes embodying them conflict with the Constitution of the United States.

General propositions do not decide concrete cases. [. . .] I think that the word liberty in the Fourteenth Amendment is perverted when it is held to prevent the natural outcome of a dominant opinion, unless it can be said that a rational and fair man necessarily would admit that the statute proposed would infringe fundamental principles as they have been understood by the traditions of our people and our law.

The text is shortened and internal citations are omitted. Note that Social Statics was a popular contemporary work on laissez-faire economics.

Holmes's bolded statement failed to carry the day. But Lochner was overruled implicitly in 1937, and explicitly in 1955, with the Court holding, unanimously, that "[t]he day is gone when this Court uses the Due Process Clause of the Fourteenth Amendment to strike down state laws, regulatory of business and industrial conditions, because they may be unwise, improvident, or out of harmony with a particular school of thought." Williamson v. Lee Optical, 348 U.S. 483 (1955). This note is broadly in line with Holmes's dissent.

From this, I would argue that the Constitution enshrines many significant capitalist principles, but not a specific mode of capitalism, and not unregulated, pure capitalism.

Note that this is a hard thing to disentangle from politics. Some conservative commentators disagree with the analysis I have given you, but I disagree with them in turn, for reasons that are beyond the scope of the sub :).