That's not really the case though.
We had a similar QE in '08 with pretty much no effect on CPI [1] or Housing [2]. As well as the increase in pricing has occurred _when the money printing stopped_ and not _while the money was printing_ [3].
The current inflation isn't caused by money printing. It's caused by pricing power by conglomerates. We've allowed energy companies to join together and they've agreed with OPEC to cut production to lead to price increases. We've allowed rental companies to join together and raise prices. We've allowed meat companies to join together and raise prices. The lack of anti-trust enforcement along with a trigger (Covid) is what caused inflations, companies realized they had a talking point (supply chain problems) that they could pin price increase on regardless of if it was true.
[1]: https://fred.stlouisfed.org/series/MEDCPIM158SFRBCLE