Yes, I was oversimplifying by saying "printing" but most people don't understand the money supply which can also be changed by fractional deposit rates, interest, etc.You are on the right track, but inflation is caused by expanding the M2 faster than productivity (change in GDP per person over a 5 year average). With their tight money policy, the Fed has been shrinking the M2, but productivity is only a little over 1% these days. A couple of years ago, they increased the M2 about 20% (if I remember right) during the covid scare.
But adjusting for GDP or productivity is still really inflation it's just inflation that is hard for the average person to see. The better policy would be a set money supply as it would automatically adjust to the new value created, etc., without a person/committee/economist deciding the "right" amount of value for a dollar.