Imagine a thought experiment:

The Federal Reserve Act gets changed, and the Fed is able to print dollars to buy Treasuries directly from the Treasury, rather than on the secondary market.

Congress says “awesome!”, and decides to send everyone $5k stimulus checks. They sell the Treasuries directly to the Fed, and the Fed buys them with electronically-printed money. No banks as intermediaries, no secondary market purchases.

The stimulus checks get deposited by the Treasury into everyone’s bank account. Their banks then get the cash as an asset, and have new deposit liabilities to their depositors in equal amount. The money is freely spendable by the consumers.

When banks get that money as new deposits, they hold it as cash until they do something with it (like make loans or buy securities). Other than a trivial amount of vault cash, banks keep all their cash on deposit at the Fed.

So, as the Fed-funded stimulus checks go out, bank reserves at the Fed would go up. The Fed ends up with more Treasuries (assets) and more reserves (liabilities) on their balance sheet, just as if they had bought the Treasuries on the secondary market instead.

In other words, it wouldn’t mechanically look any different than this: