There have been lots of arguments about what are the required factors to start an industrial revolution. Lots of things have been considered essential by some authors and not so many by others. But there's one factor which is absolutely essential.
The key to an industrial revolution is having a product or products for which the demand is extremely large (including sufficient consumers who can afford to buy it), and where reducing the price for the product (by making production more efficient) increases the demand by a significant amount. This means that as producers become more efficient, they can sell much more of the product(s), and more consumers are able to afford them at reduced prices. This leads to a virtuous circle where increases in efficiency of manufacturing in turn drive increased demand. This essentially limitless demand, over a long enough time period, is essential to driving an industrial revolution.
Historically, the industrial revolution was driven by two such cycles. One was textiles, the other was a coal-iron-steel complex where increased technology and efficiencies in the use of coal allowed greater scale of iron production, which in turn promoted demand for more iron and steel products (including some used to make coal mining more efficient). It wasn't steam engines per se, though that was part of the process; it was the whole package of ever-increasing production and reduced iron and steel prices in turn driving increased demand by making it possible to use iron and steel in many more products.
So for an alt-industrial revolution, you need a similar cycle of having an effectively limitless demand for a product(s) which continues for long enough to foster an industrial revolution. Despite having some surface similarities, Song China didn't actually come close. In Song China, there was a large demand for iron & steel, driven largely by the massive consumption for the military. (And some other spin-offs). The military demand for iron was large, and it led to significant iron and steel production, including use of coal etc, and some large-scale iron producing enterprises. But while the military demand for iron and steel was large, it also had its limits. The military needed a large amount of iron and steel each year, but it didn't need a boundless amount. Efficiencies in production meant that better iron producers could capture a larger share of the military demand, which was good for them. But it didn't increase the overall demand for iron and steel by enough to drive an ongoing industrial revolution.
So the key questions for asking where an alt-industrial revolution can emerge are:
(1) What are the product(s) that are driving nearly endless demand, and where reductions in the cost of production drive a bigger increase in demand?
(2) Where are the consumers that have sufficient capital to keep on buying the product(s), including factoring in transport costs?
And to a lesser degree, (3) What constrains someone else from producing those product(s) in other regions, since that would otherwise cut into the demand enough to hinder the emergence of the necessary virtuous circles in production.
Answer those questions, and you're most of the way there to answering how an alt-industrial revolution can emerge.
