Why the inflation and rising commodity prices when the level of GDP is still lower than potential GDP?

Since the summer of 2020, the prices of commodities and intermediate consumption have risen sharply, driving up inflation sharply also. This may come as a surprise, as the level of global GDP is still below the level of potential GDP (or the level of GDP that would have been attained without the COVID crisis). Rising commodity prices and inflation despite a still-low level of GDP require: Either the supply of commodities and goods and services to have be en reduced by the crisis; Or demand and production to have shifted from services to goods. We note that: Oil production has fallen, but not that of other commodities; The participation rate has fallen, and therefore so has the supply of goods and services, in the United States; The structure of demand has shifted towards goods.