250 years

They're wrong, and so are you. The United States did not exist in 1775. That's not arguable--its a basic fact, which all my third graders know.

Tom might be going off the belief that the US Army started in 1775 as the Continental Army, but continued as the US Army once the nation was officially formed. That's interesting since there is no mention of the United States Army until it is designated as such in the Constitution. 

Basically, the Continental Army was the first standing army for the 13 colonies, who weren't actually the United States yet, so they couldn't call themselves the United States Army.  The US Army succeeded the Continental Army, but apparently the United States government  saw 1775 as the beginning of the US Army when the Continental Congress voted to start a standing army. 

Technically the C.A. was the first standing army, but not officially known as the US Army until 1784 in the Constitution.  

Valid argument could be made either way, I guess. 

There couldn't have been a US anything before the US was created. That's kind of basic, though it eludes stupid Tom.

But let's take a good, close look at 1775. At that time, even the Founding Fathers weren't all-in on the idea of creating a new country out of the colonies. Many of them were still of a mind to achieve parliamentary representation, fairer taxation, and a level of autonomy ("home rule")--but still as loyal British subjects. It was only after the events of that year and part of the next transpired that full independence became the goal.

THEREFORE...

The Continental Army was never meant to be a permanent force. That's why the time expected to serve was so short...causing Washington to lose over half his army when enlistments expired. The idea of a permanent, professional standing army postdated the Revolutionary War.