Interest rates don’t need to change significantly for the boom to be set in motion. They just need to be lower than they would be on the basis of people’s time preferences. The Fed sets the boom in motion by monetary inflation through credit expansion within a fractional-reserve banking system. When the Fed buys assets from banks and pays with reserves, then banks can create credit by issuing fiduciary media. Banks decide how to lend the funds they create across the different loan opportunities. Having exhausted these, other investors will alter their supply of credit to take advantage of arbitrage profit. As you point out, the end result is that interest rates throughout all possibilities are lower than otherwise.
Interest rates, however, are not just earned on investment in financial assets, but also in physical assets. The rate of return on production and investment will be lower than otherwise also. But, in order for that to happen, buying prices of inputs must rise relative to selling prices of outputs. In other words, higher-stage prices must rise relative to lower-stage prices.
People obtain more money to spend on goods from the monetary inflation set in motion by the Fed through the fractional-reserve banking system. The newly created money drives demands up disproportionately on higher-stage producer goods. Consider the following illustration. Credit creation leads to more auto loans. Increase demand by auto customers pushes up auto producers’ revenues. They increase their demand for inputs, including steel, and their demand for capital capacity, including auto factories. The additional demands for steel increase the revenues of steel producers who, in turn, increase their demand for iron ore. and their demand for steel mills. The resulting increase demand for iron ore is relatively greater than the increase demand for steel which is relatively greater than the increase demand for autos.