If "multiple steps" take 400 years, then the cause is something else.
Yes, at each step keeping the 3% growth needed things to keep going, but the big thing was unleashing the nonzero growth rate, to get unstuck from the local minimum.
This is history not science so it is super incomplete.
We definitely know that the trajectory of the industrial revolution was kicked off at the plague.
We don't fully understand why there major growth periods at other times that quickly fizzled out, and what is different.
What separates those periods from the plague to the industrial revolution is a super interesting question for economic theory.
Yet, the causal chain is clear that the plague kicked off a period where investment and compound interest began to pay off, that continues to today.
However, economic growth was basically flat before the Black Plague, and increases were basically random events that went back to Malthusian dynamics.
Only since the Black Plague has the world enjoyed exponential economic growth.
Most people talk about the industrial revolution, a lot of other comments talk about the british agricultural revolution before that, but economic historians have identified the inflection point at the black plague - that's where compound interest really started to be a driver of growth, it barely existed before that, at least on long time scales.
Why other events did not have the same effects are very interesting questions for economic history.
<quote> One cannot, of course, “know” this in the same way that one can know the date of the battle of Poitiers; applying economic analysis to the spotty record of commerce during late antiquity is a tricky business. However, as can be seen in a subtly reasoned 2003 paper by two development economists, Ronald Findlay of Columbia and Mats Lundahl of the University of Stockholm, it is compelling, as well, despite its reliance on a number of simplifications. </quote>
This would be like saying "well drunk driving doesn't cause accidents because I drive drunk once and didn't get in a crash"