One thing Europe can lay claim to is the steam engine, because the British had deforested so hard they needed to mine for coal and a machine that could power a pump with coal to drain the accumulating water from the mines was actually useful enough to find support.
But once we get into the further progress of the industrialisation, I'm pretty sure gunpowder enters the equation (jog my mind, I dimly remember some synergy between developing better artillery and developing the methods to create smoother cylinders, which helped with creating better steam engines).