In various areas, they did! Though "what did those look like" is a very broad question, as is how they compared with the rest of the world, considering various people's technologies changed over time and Chinese technology spread. I'll focus on iron, coal, and textiles as given their importance to the industrial revolution, there has been a lot of work comparing those to Europe. This certainly holds in other areas, like porcelain, which Europe wasn't able to replicate until the 1700s, or crossbow triggers, where the Qin had an amazingly intricate cell like system of large scale semi-private factories producing them.
This is going to have a lot of random details on production, because you asked how it worked, because economic history too often ignores details in manufacturing, and because I love it (this is the most important reason lol).
China was the first civilization to discover cast iron.
In terms of actual production, iron ore was first smelted at a furnace into pig iron near the sites of the mines, then transported to foundries where it was recast into finished products. There is little evidence of how the initial smelting happened pre-Han, but during the Han this took place in large blast furnaces. In foundries, we have evidence of free standing copula furnaces. Pig iron was melted above a flame, produced from charcoal at this time, then poured into molds through a taphole one enough had melted, then the hole replaced . Air was blown through a pipe called a tuyere across the top. Molds could be quite complicated: clay was placed in a pattern box or "mother mold" made of wood, stone or metal, plastered with straw-tempered clay, dried, then hinged. Very complex one off molds have been found, but for mass produced implements stack molds were used, where molten iron was poured down the central shaft the molds shared, then spread over the shape of the implements created. They further knew how to make malleable cast iron by the 3rd or 4th century BC if not earlier, involving an annealing process of high heat treatment over several days, which in an oxidizing environment draws carbon to the surface of the iron burns it away, reducing the carbon content in the iron, strengthening it. Cast iron was discovered in the 14th century in Europe, with malleable cast iron discovered in France around 1670.
I've talked about cast iron's economic impacts before:
There is evidence of wrought and bloomery iron production in the periphery to the north and west quite early, as well as Korea, perhaps being transmitted from the Scythians. Cast iron was discovered as early as the 5th century BC, probably in Southern China, perhaps in Wu in the Yangzi river delta, possibly for making agriculture implements. While early cast iron was not as strong as wrought iron, it was even cheaper. As this was happening, the control the Eastern Zhou state had over their vassals was evaporating, leading to centuries of war during the Spring and Autumn and Warring States periods. This led to a shift from chariot focused aristocratic forms of warfare and a decline of the patrimonial, almost feudal, state to large scale infantry warfare and increasing centralization of state control.
In order to arm these new infantry armies, states turned to iron. They set up massive, tightly supervised weapon producing manufacturers, and leased mining rights to individuals, producing massive amounts of wrought iron and steel. Qin undertook widespread forced migration of skilled workers to set up industry in newly conquered areas, some of whom became wealthy industrialists. Cast iron farm implements combined with large scale state led irrigation projects led to an increase of the productivity of farming, and peasants also started using iron for pots and cookware. While cast iron is generally weaker and more brittle, by the ~3rd century BC China knew how to cast a stronger malleable cast iron through subjecting cast iron to a multi-day heat treatment. Furthermore, it didn't really matter for some products such as cookware, while others, such as plows, would have a detachable cast iron edge that could be easily replaced if it broke.
So in the mass production of iron implements, especially for widespread use among the peasantry, advanced manufacturing was quite important.
##The expansion of the iron industry and use of coal
There is very early evidence of coal use in and on the northern edges of China. By the time of the Han, there is evidence of use of coal in manufacturing both ceramics and iron. But it is only in the Song, when increases in iron production for both a growing military and farming population, heating homes in the north, and more put enough pressure on timber resources to make coal economical, did it start to see widespread use in iron production. The scale of both industries at this time (and until quite recently) is very unclear. One of the earliest estimates of iron put it at 110,000, estimated by Hartwell based off of tax receipts in Shandong, then assumes 10% of all iron was taxed, and arrives at 110,000 tons of iron per year. As you can probably imagine "assume 10% iron is taxed" has been argued a lot about, and there is a range of estimates after from 1/3x to 2x that. Something similar occurs in coal, where it is just unclear the exact scale of production during or after Song, to the point where various sources argue that it declined, and others that it increased. Regardless, the scale of iron production was absolutely massive, Hartwell's estimates possibly put it at greater than all of Europe in 1700.
There are problems with using coal in iron production that had to be overcome. First, bituminous coal, the most common type, gives off noxious, tarry gas when burned. This can cause all sorts of problems, such as tarry build ups sticking the sides of the furnace, then collapsing when the build up too much, which can destroy the furnace. Furthermore, sulfur in the coal can be introduced into iron, critically weakening it. Anthracite, hard coal, is purer and doesn't have these problems, but is also rarer-perhaps 12% of China's coal reserves. In Europe, this was overcome with the discovery of coke, and a century long process of figuring out how to build furnaces that can burn coke. Limestone was added to bind the sulfur and prevent impurities in the iron.
Coke is made by putting coal through a similar process of oxygen free heating as making charcoal, and results in a much cleaner coal. China probably knew how to make coke in the Han, certainly by the Tang. The evidence for this can be hard to parse, as the similarity of the process to making charcoal, and similar names can make the two indistinguishable. In the Tang there starts to be clear evidence, for example a Daoist handbook gives processes for making charcoal for alchemy, and explicitly includes coal (to the point of mentioning stone) along side wood as being treated by fire for a period of time, which can only be the process of making coke. By the Song, there was clear evidence of coke being used to make iron. Unfortunately, basically none of the technical details survive. We are not sure how and if they were overcome the various challenges that took the English over a century to do, we just have to rely on the English experience for that. Following the fall of the Song and the years of chaos that followed, much of the iron industry was relocated and probably used charcoal. It is possible that this was due to the weaknesses of the resulting iron, that they either never fully overcame the technical challenges of using coke or it was lost in the periods of disruption and chaos.
The last was quite believable, because the networks of literate people describing these processes didn't extend to artisans. In their defense, literati were often quite interested in manufacturing and agriculture and wrote down high level details, but not precise manufacturing instructions for things like iron. This would have been passed down among artisans, and thus could easily be lost when northern China was invaded or when the Yuan collapsed.
None the less, the Song were able to use coal and coke centuries before Europe to help avert a fuel crises caused by civilian and military demands.
edit: On coke, I'm wrong, see the comment by /u/ParkSungJun here