Who paid for that $4.5 trillion balance sheet?
"Money" in this case is a liability of the Federal Reserve - mainly reserve balances held at the Fed, but also curency in circulation (which was largely stable).
Like any other entity, the Fed creates liabilities by issuing them. It did this by buying bonds in the open market (mainly Treasury and mortgage securities).
- The seller of the bond (more likely, its bank) will get a deposit ("money").
- The Fed gets an asset (the bond).
As people have found out, there is little to stop the Fed from doing this. They get matched assets and liabilities, and the assets it buys pays a higher rate of interest than its liabilities.
Other entities have to worry about funding risk when conducting such trades -- others may fear bankruptcy, and not lend them money. Very few people worry about the central bank running out of money.