If a bank has $100, they can write a loan for $1,000; effectively putting $900 more into circulation. When that is spent, it gets deposited into a bank, which can then loan it out amplified again.

Since there is not infinite money, there must be a gap in my understanding somewhere.

While this is true, the only “new money” created in that loan is the interest becase the capital is paid back , albeit over decades.