They wouldn’t have to get it right ‘one time’, they’d have to get it right continuously for quite some time, and still let the damage they caused in the past repair itself.
You’re going to have to learn basic economics and then read the intellectual literature devoted to these topics. No one is going to give you a completely adequate response here, it would take way too much time and simply isn’t worth it. But creating inflation, that is, expanding the money supply, requires a drop in the rate of interest. If the rate of interest remained the same, then there would be no demand for inflation whatsoever. Business cycles have to do with capital, not with consumption, employment, or fancy aggregated indices. So again, inflation means a fall in the rate of interest below its equilibrium position.
They don’t really set the market interest rate for loans. They simply control the money/credit supply. The only way for them to get it right is for them to close their doors and become another federal museum.
Actually their rates match the Treasury bill rates pretty well (I forget whether it’s the 4 week or 3 month bill they target). Usually the rates they set lag the market by a few weeks. For a beautiful illustration, see page 56 (fig. 17) of this ebook by Robert Prechter: