The answer is largely going to hinge on just how "flexible" you are with your definition of "industrialization." You're going to have to be pretty flexible, because in most of the ways that most people define it, the answer's a pretty solid "no." But hey, let's go over the pros and cons and see where we wind up:

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Economic Growth
Song China undoubtedly experienced a degree of economic growth and prosperity that would be unmatched in the world until the 18th/19th century European Industrial Revolution. Its zenith is generally agreed to be the reign of its 6th emperor, Shenzong (r. 1048-1085). As always, it's virtually an effort in futility to try to "compare" vastly different economies across huge swathes of time and space, but the figure most generally put forward is that Northern Song in the mid-to-late 11th century controlled something like 25-30% of the total global GDP.

This tremendous growth came about, in significant part, because of a rather revolutionary reform to the taxation policies of the realm. Prior to the accession of the founding imperial brothers, Taizu and Taizong, dynastic taxation policy had been based solely around head and land taxes. That is to say, you'd pay annually for the number of people in your household, and the amount of land that you owned. The philosophy behind this is complicated, but we can boil it down to it being a fundamentally different economic philosophy that anything we're used to, namely: that growth was neither the goal, nor even particularly desirable; instead stability is what should be sought in the realm's economic planning. Of course, this tends to hit a brick wall when something unexpected (like a foreign invasion, natural disaster, or massive internal rebellion) crops up. Taxes tended to therefore be raise on the peasantry... and again... and again... until it was too much - ipso facto, there's you cause for rebellion.

So, that shifts under the Song policy to a policy of "hey maybe let's not tax the pants off of the peasant farmers, and instead try something craazy." That "crazy" idea is to tax trade - both internal & with foreign entities. And there's a lot of pushback on this, since it generates crazy profit, which both makes the economy unstable and also makes the Confucians in the government feel all icky because they've got a real problem with commerce in general... but on the other hand, hey, profit is profit. It works like gangbusters.

This massive economy led to rich trading ties with a large number of its neighbors - including Japan, Korea, and the Indian Ocean marketplace. But the most significant economic ties across the totality of the Song Dynasty would be those not of its own making. Rather, they would be it its competitor and rival states to the north - first the Liao Dynasty of the Khitan People, then the Jin of the Jurchen & the Tangut of Western Xia, and finally (& fatefully) the rising might of the Mongol Khans. Across the vast majority of its lifespan, the Song Dynasty's emperors - both Northern and Southern - were devoting an absolutely tremendous percentage of its yearly GDP toward paying "tribute costs" for those northern powers to cease attacking it (it would then proceed time and again to shoot itself in its own foot on that front, but that's another tale).

Evidence of the efficacy of this economic shift play out in the straight monetary numbers. In 964 CE, for instance, export revenues were recorded as totaling 500,000 strings of cash-coins. Just a little more than 2 centuries later, in 1189, records show those export revenues at an incredible 65 million strings of cash.

Population & Urbanization
The Song Dynasty also saw a China far more urban than that any that had come before. Multiple cities across the empire could boast populations in excess of 1 million, sometimes even simultaneously. For instance, if one considers both the Jin capital of Zhongdu (mod. Beijing) and the S. Song capital Lin'an (mod. Hangzhou) to be "Chinese" cities at the same time (even as they're under different regimes), then they're both >1M at the same time. Increased urbanization leads to, of course, further upticks in technological innovations and novel distributions of labor. Other major urban centers included Kaifeng and Liaoyang.

This urbanization combined with a policy of much freer movement among the populace led to another new need: a place to stay when on the move. Hence we see the effective "invention" of the concept of the motel as a stable business in this time period, as well.

Technological Sophistication
Song China absolutely sees an - er'hem - great leap forward in terms of science and technology. Here's a partial list:
- moveable print typeface - ca. 1000 CE
- mechanical water clock - ca. 1090 CE
- paddlewheel ships - ca. 1135 CE
- magnetic compass - ca. 1150 CE
- water-powered textile-production machinery - ca. 1200 CE
- large (~200-600 tons) seaworthy transport craft - ca. 1200 CE

Though paper was a much older invention (with industrial-scale production beginning ~ a millennium earlier in the mid-Han Dynasty), by the Song it had become such a staple, and so cheap to produce that it was used for things far beyond books, such as:

toilet paper
tea-bags
disposable/single-use "advertisements"

Gunpowder likewise far precedes the Song, though it is during this period that it is effectively weaponized into things like grenades, flashbombs, and gas bombs, rocket arrows, flamethrowers, and even primitive forms of "torpedos" (Not to mention the much more fun application as fireworks).

Production
You ask about mining, as though that is a specifically "industrial" action - but that's not the case. Mining far, far precedes industry (and is, in fact, an absolute prerequisite). Mining during the Song, though, was absolutely done by man and animal power, and hydropower where available - but no jackhammers here.

In terms of iron & steel production, Song output was - no huge surprise here - by far the largest in the world at the time. Estimates based off of tax receipts suggest that it may have been producing as much as 125,000 tons (127M kg) of iron per year by 1058 - a figure that would be surpassed by Great Britain only in the 1840s.

The Mongols while invading Song Dynasty China, destroyed what some consider to be the first signs of industrialisation. What was the state of industrialisation in the late Song Dynasty China? How much did they utilise steam power and mining? How was the quality of life in their factories?

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