Yeah, but the OP didn't say it had to be decisive
But...
Andy Jackson!
Tennessee Rifles!
Buckskins!
Yeah, but the OP didn't say it had to be decisive ... just that they had to be there.
It's actually a pretty
huge point of departure for the US to be engaged militarily on the European continent in the Nineteenth Century, even more so as early as 1815 (or whenever) - basically a century earlier than historically (more or less).
It is also worth pointing out the US had been engaged (twice) in the Med by this time (First Barbary, 1801-05, and the Second, 1815), as well as the Quasi-War (1798-1800) which was largely confined to the Western Hemisphere but included some actions in the North and Central Atlantic.
So it's not outside the realm of possibility, and the influences of three (counting the two Barbary conflicts) successful US military expeditions to Europe and European waters, much less in de facto alliance with the UK, before 1820, could actually be very significant.
Hard to see the US intervening again, absent the "villains of all nations" type status of the pirates and (arguably) Napoleon as outlaw, however; maybe on the part of the Greeks against the Turks in the 1820s, along with the British, French, and Russians - sort of a "fellow revolutionaries" type of effort.
After that, it's more of a challenge, but certainly if the US had the above track record, it is possible to see the US being more engaged than historically in Europe in the remainder of the century. I doubt there would ever be anything more than alliances of convenience - the "blood is thicker than water" operations against the Chinese and Japanese, in the 1850s come to mind - but I could see a US "European" squadron to rival the Mediterranean Squadron; presumably that could lead to some interesting events in the middle of the century.
There's also the question of how such experience, along with that of the Civil War, would have an impact on the USN in the 1870s and 1880s - the "Steel and Steam Navy" might come along that much sooner.
Best,