Ah, but you didn't buy them!

This is generally the way it goes. Businesses buy rolls of quarters to fill the register, cash-using consumers "buy" bills, and gradually accumulate those quarters as the bills break down. Then, they return it to a bank to deposit them, and (possibly with a stop at the mint to retire old coins and inject new ones) the cycle continues.

Meanwhile, businesses deposit the bills they accumulate, and all kinds of wire transactions between banks, consumers, businesses and the government account for the rest of the money supply.