It’s not just about the value. Real inflation—if we don’t just accept the government’s manipulated CPI—is also difficult to calculate.
You are correct that there's no reliable metric to measure inflation. Since "inflation" comes from "inflate" which means "to expand the supply of something", then the most accurate metric would be the M2 supply of money. This is what is "inflated", and results in the rising of prices.
Since most freshly printed money is used to buy houses as a way to protect the property owners against inflation, the price of your dream house could also be a metric that measures inflation.
Interestingly, you do not even need to print money to have inflation, you will have to eventually but you do not have to when it first happens. When something gets expensive for a reason that creates a chain, you could be late to it.
Like in this case, oil got expensive because of Hormuz, and that caused logistics to be expensive, moving food from farms to table, and that caused the food to be more expensive, which resulted with everything else to be more expensive, without a need to print more money.