The trillions the Fed is printing aren't being sent out as stimulus cheques. They are being used to provide short-term liquidity (Which does not cause inflation), and to buy junk bonds, (Which does cause inflation, and also happens to prop up the stock market.) Some of that money is also being lent to the government - if those loans are paid back, they will cause net zero inflation. (Because once the money is paid back to the Fed, it is destroyed.)
This is precisely why we have central banks that are independent of government budgets. It creates checks and balances against a government choosing to print its way out of budget troubles.