The steam engine was not the industrial revolution. The industrial revolution was a major transformation of society which the steam engine merely was a one such development, and not even the most important.

The key to the industrial revolution was that it was the first time everything was advancing steadily all at the same time. Just taking a look at the steam engine, there is an approximately 200 year long process where europe went from crude steam pumps, such as Jerónimo de Ayanz y Beaumont's steam pump from 1606, to the practical steam engines that came into use in the early 1800s. Along the way there was the discovery of the vacuum and atmospheric pressure, the development of methods to measure and alter such pressures, regenerative heating systems, the concept of the piston and cylinder, the developments of manufacturing technologies that could produce seals adequate for a steam cyclinder, improvements to metallurgy allowing for the use of high pressure steam, etc. Some people will hold up Savery's steam engine or Watt's as "the steam engine" but both these and all others represent just arbitrary points in a long line of very gradual evolution.

Completely independent of the invention of steam power, you have innovations like the 4 field crop rotation, the european seed drill, the dutch plow, the mechanical thresher, new world crops, land enclosure, and scientific selective breeding which all greatly increased agricultural output, allowing a large non-agricultural population to be supported for the first time in history. Advances in manufacturing such as the development of 3 plane grinding, the metal lathe and other machine tools, and standardized threads made innovations like standardized parts, the spinning jenny, and the practical steam engine possible. A shift in the very way people thought about production lead to new manufacturing techniques for chemicals, paper, glass, iron, etc which made these goods both ammenable to the new factory system, as well as economical and high enough in quality to allow for further advancement.

All of these developments were in turn part of a broader scientific and engineering revolution, which best explains why the industrial revolution did not occur in other civilizations. While invariably every society has produced curious people who have tinkered and observed the world, typically these were brief flashes in the pan. Someone like Hero of Alexandria would come along, make a bunch of cool inventions, then die and nothing would come of it. People falsely believe that civilizations like the romans were uninterested in technological progress and thus did not think to exploit inventions, but that's simply not the case. They were very good at and excited about making money with some new technology. The issue was that the utility of inventions was what they really cared about, moreso than the invention itself. The idea of developing technology for its own sake was uncommon, to the point that the very few who did see value in such projects could not effectively collaborate.

In early modern Europe, you have a unique historical phenomenon where a century of so of religious upheaval and warfare suddenly mean the traditional status signalling methods of the nobility - military achievement and influence in the catholic church - fall out of vogue. People need new ways of socially one upping eachother, and by chance this takes on the form of the gentleman-scientist. Spending all your time and money doing experiments or making contraptions with little or no practical utility becomes cool. You get tons of incremental but consistent improvements which are widely disseminated and further built upon. You get people like Watt trying to make a steam engine with a double acting piston and it doesn't work because manufacturing methods are just not there yet, and then Wilkinson comes along and develops a boring machine that makes it possible.

Of course all these things are rooted in deeper trends. For example the aftermath of the Black Death really kickstarts Europe's development as a labor shortage forces people to use land more efficiently to maintain agricultural output, the adoption of the printing press allows practical dissemination of ideas across a continent, and the timely discovery and exploitation of the new world lets Europe avoid what likely would have been major demographic and economic issues in the 1500s, instead allowing for a period of rapid population growth and improvement in living standards.