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.
