It wasn't much later. The Fed started raising interest rates in March of 2022, and inflation peaked 3 months after that. The ability of firms to "price gouge" is evidence of monetary inflation, so I'm not sure why you'd be so opposed to interest rate hikes.
"The ability of firms to "price gouge" is evidence of monetary inflation"
Where do you get that? It's far more likely evidence of monopoly/oligopoly power.
Monopoly power isn't mutually exclusive with monetary inflation. The competitive landscape didn't significantly change in 2021 when inflation started to rise. That firms were able to increase their profits significantly during this period indicates an increase in aggregate demand, which suggests monetary inflation. Even if monopoly power was a factor, it wouldn't be able to be realized without the increase in demand.