There's another route to an industrial revolution that might have happened - steel.

The British industrial revolution was built from iron, not steel. Mass production of steel didn't appear until the 1880s, with the Bessemer converter. This was half a century after the deployment of successful railroads.

Iron and steel was known to the Roman empire. The steel wasn't very good, even by the standards of antiquity, but it was good enough for short swords and some tools. They got as far as the "bloom" process, but no further. Despite this, there was a modest iron and steel industry.

A Bessemer converter is a simple thing. It's a big iron vessel lined with brick attached to a furnace and blower. Roman ironworkers could have built one. It's the metallurgy that's hard. Bessemer built the thing, but steel quality was random at first. Robert Mushet, a metallurgist, after about 10,000 experiments, figured out how to get consistent quality from the process. The basic idea, from Wikipedia, is to apply enough heat and air to burn off almost all the carbon in iron ore, leaving pure iron. Then add 'spiegel glanz' or spiegel eisen, a "double carbonate of iron and manganese found in the Rhenish mountains" which was iron, 86…25; manganese, 8…50; and carbon, 5…25. Controlled amounts of manganese and carbon are thus put back into the molten iron, and steel comes out.

A number of cultures figured out steel by accident. Thus, Japanese steel, Damascus steel, etc.
Various trace additives - vanadium, molybdenum, etc. were used. The Roman empire got as far as mediocre steel. But the process was neither understood nor reproducible at scale. Mass production required enough analytical chemistry to do quality control on the ingredients.

So an interesting speculation is what might have happened if an early culture had some people really into finding out what stuff is made of. That leads to analytical chemistry. Some Roman philosopher might have discovered that if you grind rocks to a powder, mix with water, and spray into a steady flame, colored light comes out. If you look at that colored light through a prism, you see sharp lines, in the same places for the same materials, which indicate the elemental composition of the material. If they'd happened to talk to someone in the Roman army responsible for a sword factory having yield problems, they might have gotten some samples of the minerals being used. That might have led to the beginnings of metallurgy quality control. As there is in a modern steel plant, there would be somebody in a little room not too far from the furnaces doing analysis on the raw materials.

Steel would still be somewhat expensive, but with a repeatable production process, swords and knives would get better. Then agricultural implements and other tools. If you need to plow hard or rocky ground, a steel plow is a big help.

The next big breakthrough in an an agrarian society with some steelmaking capability would be a reaper. The McCormick reaper was the first machine that really boosted agricultural production. That's what kicked the world past sustenance-level agriculture.

So that's an unlikely, but not impossible, alternative path to an industrial revolution.