Originally, the U.S. was not intended to have a standing Army; rather an Army would be raised as necessary to fight a war and then disbanded when the war ended.
Obviously, the U.S. Army has been in continuous existence for a good long time now -- certainly since WWII. But I believe the original design was more or less adhered to early on. For example, the first U.S. declaration of war was in the War of 1812. This ended in 1814. Shortly thereafter was the Second Barbary War in 1815, although I'm not sure the Army was involved in that. Regardless, I doubt the U.S. had an army in 1816.
So, my question: what was the most recent point at which there was no U.S. Army?
After the 1849 discovery of gold in California kick-started the westward expansion, I would imagine the resulting need for frontier outposts resulted in a continuously existing army that has yet to be disbanded. So my guess is that the most recent time when there was no U.S. Army would have been in the 1840s -- perhaps in early 1846, just before the declaration of war against Mexico. But that is only a guess.
There has NEVER been a time when there was no standing land force paid amd answering to the national government.
After the revolution from 1784 it did become incredibly tiny. Enough to fit in one large room. And all they did was occupy West Point as storage for all the left over cannon and supplies from the Continental Army. Soon after though trouble with Indians led to the larger Legion of the United States in 1791 under Mad Anthony Wayne which directly was reformed after a defeat into the Army of the United States in 1796.
The 3rd Infantry Regiment (The Old Guard) who provide the guard at Arlington cemetery trace their lineage back to the original 3rd Sub Legion.
For example they fought in the Seminole Wars in the 1820s and 30s down in the Everglades which as a part of GDP are still the most expensive wars ever fought by the US.