IIRC the steam engine was intially created to drive pumps to clear out standing water in coal mines, the demand for coal was so great that finding solutions to increase the efficiency of mining was a profitable venture.

Since the engines relied on combustion of fuel, and had contributed to an abundance of coal which was far more efficient than wood or peat, they became very practical to use in other industrial settings that had once been driven by water or wind mills. This included mining operations beyond coal, including iron and other metal deposits; an increase in the amount of raw materials drove down the value of these commodities which made experimentation in their applications a less costly venture, and exponentially improved their own acquisition as many inventions had applications in mining and distribution techniques.

The whole propagation of technologies, became self sustaining, and as mentioned by /u/m15wallis, the demand for technologies and more fundamentally, raw materials, was driven by European conflict

Somebody else will probably give you a better answer, but aside from the Enlightenment itself and the development of scientific theory, Europe was pretty much constantly at war for centuries before, much like pre-Qin dynasty China, and they couldn't migrate to avoid these wars like many other groups of people could. This meant that they were constantly searching for any technological or tactical advantage over their foes, and were constantly searching for resources to grow their populations and armies in order to secure their borders from their neighbors. This meant expansion to further and further places and increasingly powerful military and exploratory tech (like the Caravel) that would enable a small force to conquer a large area and bring resources from Country A to Country B. They were successful because one nation never really emerged as the single, absolute dominating power of the continent for an extended period of time (Britain came close, but still wasn't an ironclad hegemon that prevent other nations from searching for a way to beat them in some manner), and so there was constant innovation by various actors in order to be better than their neighbors so they wouldn't be killed by them.