That's .... really not correct.

Let's start with the revolutionary wars. About 200,000 Americans picked up arms during the revolutionary war, which is a lot! Especially next to the 121,000 troops the British had in 1781.

Except that 200,000 is wartime total, while the 121,000 figure is all at once in 1781. The average number of men under arms that the Americans had was about 40,000, roughly on par with the 48,000 committed by the British in the colonies. Keep in mind that this was a demobilized and underfunded British army, with the British coffers being empty after the 7 years war.

There are a series of battles on the continent that would see more men committed to a single battle than the Americans had under arms at once during the revolutionary wars. The Prussians (Germans to you and I) committed 20,000 to the Battle of Mollwitz in 1741, and 36,000 to the Battle of Hochkirch in 1758. The Austrians committed 80,000 to that exact same battle, twice the number of Americans under arms twenty years later.

By 1776 Frederick the Great would have 187,000 men under arms during the peace.

There is a very good reason why the founding fathers wanted to remain aloof from continental interests.

The US Civil War is the bloodiest war that we've participated in, because every casualty was by necessity an American. It was a much larger conflict compared to the revolutionary war, but it doesn't really stand out as conflict containing large armies, compared to other European conflicts before and after.

2,200,000 Americans fought on the Union and 750,000-1,000,000 Americans fought for the Confederacy during the war. The estimated peak size of each army was 700,000 for the north, and 360,000 for the south. So we're an order of magnitude up from the revolutionary era, how does this compare to other wars on the continent?

.... Not good, as it turns out. The French revolutionary government managed to get a peak of 800,000 men under arms during their various wars half a century earlier. The Napoleonic wars saw 1,200,000 men under arms on the French side at once, with roughly 1,450,000 British, Prussian, and British soldiers arrayed against them. Napoleon dragged 685,000 men into Russia (and left half of them there...). To put that into perspective, he dragged the entire Union army into Russia, and then left the entire Confederate army dead on the outskirts of Moscow, then he kept fightinng.

Heck, even previous conflicts dwarf the civil war. The 30 years war (1618-1648) saw armies of roughly half a million squaring off for 30 years.

The Franko-Prussian war (1870-1871) saw a max of 950,000 Germans (we can call them that now) squaring off against 710,000 Frenchmen at once.

Side note: the one thing the Civil War has going for it is that it previewed the horrors of WW1 much better than the napoleonic wars did, even if it was smaller. Better artillery and better rifles started showing up by this time, including limited numbers of repeating rifles. Apparently the European powers sent observers to see how this would all work out, and if that's true then holy crap did they not learn the right lessons.

And between these large conflicts you find .... nothing. From 1800 to 1810 the US had less than 10,000 men under arms total (excluding reserves). You see a nice little spike of 20,000 or so around the war of 1812, having your capital burned will do that to you, but it's all kind of cute compared to the millions of men under arms trying to kill each other in Europe at that exact time. The numbers remain in the 20-40k range until the Civil War, and then it climbs into the heady territory of .... 50,000 men and slowly climbing. At the start of WWI the US had 130,000 men under arms, less than half the number of casualties that the French would suffer in the first month. The first battles of WWI would show the French and Germans committing twice as many men to a single battle each as the US had available in total.

Of course, we know how this ends. The US eventually builds up its army and comes in to finish off an exhausted Germany. Then we start keeping larger and larger armies until today, when we outspend the next 7 countries combined. Nowadays we absolutely do keep a very large army, but from the very beginning? Not so much.