Possibly, though printing off $40,000 for every tax payer then cutting them a few thousand is probably not going to be the best approach.

https://fred.stlouisfed.org/series/M1REAL

Where did you get $40,000 from?

5.3 Trillion in stimulus divided by 150 million people who pay income tax in the US is actually $35.3k USD. The final stimulus toll may be higher and taxes come from a variety of places so that may be high for the final burden per person, but I think it will be close by the time all is said and done.

The stimulus checks, unemployment benefits, at least 85% of PPP money, and education funding all solely benefit regular taxpayers. Large corporations got the equivalent to subsidized loans. Let's say that random pork projects benefit both groups equally. I don't see how regular taxpayers are losing out here.

This is risky, because if the fed accidentally injects too much money by buying back too many bonds, they can always un-inject it by selling the bonds back (and banks are compelled to buy). This lets the fed be more aggressive because it knows that if it goes too far and starts seeing more inflation than it intended, it can always walk back its decision. But there's no realistic way to do that after having given $1000 to every adult.

Taxes?

The Fed can't make taxes. Congress makes taxes, but Congress is subject to popular approval, and the population don't like tax hikes.

The Fed also can't give $1000 to everyone.

Changes in tax rates require Congress to act. Too slow moving to be a money supply control.