Should the Federal Reserve have reacted earlier to inflation?

The Federal Reserve is now being widely criticised for not reacting earlier to inflation in the United States and for letting it become very high (7.5%) in early 2022. But could the Federal Reserve have reacted earlier to inflation (in mid-2021, for example)? It is true that the nature of the inflation in the United States is worrying, given in particular the significant role played by rising profit margins in that country; But to combat inflation, the Federal Reserve would have had to raise interest rates above the level of expected inflation. This would have led to a sharp spike in real interest rates and would have sent the US economy falling again just after emerging from the COVID crisis. So it is understandable that the Federal Reserve spurned such a policy.