Suppose everyone in new United States woke up one morning keenly resolved that their country should be infamous around the world as a badass fighting nation that goes wherever the scrap is, and picks some when everyone seems too tired to fight?
Just what could they do, on a world scale, in the early 19th century?
I seem to recall Alexander Hamilton, in the Federalist Papers, rather tipping his hand that he for one would have liked a robust, active foreign policy where the USA makes strong alliances with European powers, getting into the game there; it was in the Letters regarding the proposed Constitution's provisions for Federal army and Navy.
The reasoning for it would be the flip side of the argument the USA should stay out of trouble because we weren't very strong compared to nations like Britain, France, Austria, Spain or Prussia--precisely for that reason, an advocate of a scrappy foreign policy would say, we need to cultivate strong allies in Europe who can make any of these powers (realistically in this case, just Spain, France and Britain, the sea powers--most realistically just Britain) think twice about attacking the USA optionally.
But to cultivate an ally, we'd need to be useful to that ally. Realistically unless we managed to shift over to allying with Great Britain, what a European power could expect of the USA would be "you Yanks go distract the British in Canada, maybe get in a bit of privateering against West Indian commerce while you're at it." Even if the United States were to scrape up substantial armies, we wouldn't be able to deploy them overseas against British opposition.
Allying with the British is somewhat different, but a Patriot might reasonably ask, what the devil did we fight and bleed so much in the Revolutionary War for if we are going to once again dance to a London tune?
During the Napoleonic War period, the Federalists did tend more and more to favor the British side, while the Democrat-Republicans favored France. So Hamilton may well have been thinking that the purpose of American independence was to secure negotiating leverage and respect in London for American interests, but that on the whole with that sort of more equal partnership established, Britain would be the right side to be on. Otherwise his hopes for a really strong American Navy would seem rather foolish, as the RN would grind them down.
Either way, the United States is not really in the game. As an ally against Britain our role is pretty much dictated by geography, to try and win Canada if we can and see how disruptive of British commerce our privateers can be, bearing in mind that in the interim our own commerce with the larger world is pretty much terminated. In 1812, fighting just such a war for our own reasons, at a time when the British were quite distracted already, we didn't do so well!
The alternative of supporting Britain is more or less the course we actually took on the whole. A more "active" foreign policy on those terms means pretty much sending troops and token naval forces (even if substantial, they'd be token, though perhaps appreciated, compared to the total sails of the RN!) wherever the powers of London thought some application of force was in order. Since the British weren't in any wars they had trouble handling simply for reasons of scale between the Napoleonic Wars and the Great War, the OTL American policy of sitting back, fighting only in our own backyard, and letting the British handle British interests, seems smart to me.
In the context of the North American continent the USA OTL was about as bloodthirsty as anyone could wish for, and considerably more so than a lot of people wished!
I'd say we ceased to be "isolationist" at about the right time.