The Fed can purchase Securities directly through Open Market Operations (FOMC IIRC)
Not to mention Buying the loan from the Broker-Dealer at the Discount window etx etx
That's true. But they can only purchase them from approved dealers, not the Federal government.
This means that the bank in my example would have to buy the Treasury securities first, so that the Fed could buy them through a Permanent Open Market Operation (POMO) - and then create Federal Reserve notes as liabilities against the securities.
How would the bank afford the $2,000 on new securities in my example, without using some of its loan papers as assets for the purchase?