What?
the US Mint in the US Department of Treasury creates money (which it then banks in its account at the federal reserve), though perhaps the ebb and tide of money into and out of the economy is more like what you describe?
The primary way money is made is through loans, though the Fed buying treasuries also creates large amounts of money. When you deposit at a bank, they're only required to create a fraction of that deposit available. Hence - fractional reserve banking. [1] You deposit at a bank, they take that deposit and lend it out to somebody who now spends that money which eventually ends up getting deposited at a bank again, and the process iterates. If at some point everybody demands their money, a run on the bank, which the bank could not afford as they've lent out deposits to other people, then the Fed bails them out.
The exact process is slightly more subtle, but not fundamentally different. There's a lot of great videos on a search for 'how money is created' at any video site. Because it's a question few know the answer to, everybody wants to know the answer to, and the answer itself is somewhat unsettling.
[1] - https://en.wikipedia.org/wiki/Fractional-reserve_banking
"The actual process of money creation takes place primarily in banks." [0]
[0] https://en.wikisource.org/wiki/Modern_Money_Mechanics/Introd...
Here's where money is physically created, somewhat of a curious point since so much of transacted 'money' is digital, and perhaps why the article above misleadingly says "creates".