Others are better placed to comment about the policies of Ptolemy VIII Euergetes II, but I just want to point out that the notion that Alexandrian scholars in the 2nd century BC "were only about 300 years from full on industrialization" is completely incoherent.
Firstly: while inventions like the steam engine can be seen as markers of linear technological progress (from simple to more complex machines, etc), industrialisation is a historical process. It is not linear; it doesn't simply happen because someone invents the right machines. Even in the actual age of industrialisation, with the technology readily available, only some parts of the world actually industrialised while others either struggled to keep up or took no part in the process at all. Even within industrialising European nations, industry tended to be concentrated in a few heavily urbanised areas with good transport links, while much of the country remained at first unaffected.
This is because technology is only one element of industrialisation, and arguably not even a causal one. The process doesn't happen because of new tech; new tech is invented to facilitate the process. The actual causes have more to do with the availability of certain resources (capital, labour, ingenuity) to meet certain economic and political challenges within a global network of trade and colonialism. Without this complex system of factors in place, industrialisation could never have happened anywhere. Plunk a fully functioning steam engine down in Bronze Age Mesopotamia and I guarantee you that absolutely nothing will happen.
Indeed, this is more or less what happened in Ancient Egypt. A rudimentary steam engine was invented there in the 1st century AD, a few centuries after Ptolemy VIII. But with no practical application, economic purpose, or socio-political value, the machine remained nothing more than an amusing toy for philosophers. There was no force that might pull the steam engine into the service of industrialisation, so it did not happen.
Generally, the role of philosophy in the ancient world must not be confused with that of science in the modern world. People didn't apply learning to solve problems and improve daily life, but to understand the essential features of the universe. By definition, philosophy was unconcerned (and prided itself on being unconcerned) with the everyday. Applying philosophy to practical ends was called sophistry, and was sneered at by the likes of Plato and Aristotle. The learned men of Alexandria busied themselves with abstract geometry, poetry and grammar. They were not trying to create a better world, but to escape from it to a higher plane of understanding, in which the nature of humanity and the intentions of the divine would be more clear.
In other words, there is no way in which the scholars of 2nd century BC Alexandria were even on a course toward industrialisation. Nothing in their state or society prompted any such development, and if it had, they would not have been interested. If you could go back in time and give them all the tools of modern industrialisation, they still might not change anything about the way Ptolemaic Egypt worked, because why would they?
Secondly, the idea that we could estimate the time by which a society with a given level of technology would "reach" industrialisation is completely absurd, antihistorical gibberish. In order to claim our 300 years from Ptolemy VIII to industrialisation, we would need to know exactly which steps needed to be taken and how long each step would take, assuming (for literally no reason) that each step would immediately be taken when it became possible to do so. Such claims rest on a notion that technological progress is both linear and measurable, progressing at a certain speed along a fixed path with known points along the way. Things may work this way in computer games but they do not work this way in reality.
It is easy enough to see why such a claim is nonsense when we look at actual industrialisation in history. Take England. English industrialisation was a slow process to which I'll attach the arbitrary dates of 1780-1850 (the period isn't really fixed). Go back 300 years: we are in the time of Henry VII, first Tudor king. Would anyone look at Late Medieval England and say "yep, these guys are 300 years away from industrialisation"?
Japan industrialised in the Meiji Era, starting in 1867. Go back 300 years and you're in the middle of the Warring States period, with the whole country in turmoil and the Portuguese just arriving. Again, would anyone examine this period and assert that this place was no more than 300 years away from railroads and ironclads?
Even if we assumed that Alexandrian scholars were doing their level best to advance the technology and change the manufacturing processes of Ptolemaic Egypt, there is no knowing how long it would have taken them to industrialise. Again, technology may progress from one invention to another, but industrialisation is a historical process, which does not drive itself. It depends on countless other factors, most of which have nothing to do with learning and technology, which cannot be anticipated or forced, and which expose the kind of counterfactuals of that AskReddit thread as the ignorant speculation of people with no sense of how human history works.
/u/Iphikrates did a really good job explaining the nonlinearity in development and the importance of technology embedded in society.
However, I disagree on the aspects of science and technology. Just assuming because the demand is there due to trade or colonialism, isn't enough to drive everything that follows.
None the less, the conclusion is the same: they weren't close.
The steam engine is a good example. The first practical steam engine, the Newcomen engine, was an atmospheric engine. It relied on a condenser, which condensed steam through the injection of cold water, creating a vacuum, which drove the motion of the engine through atmospheric pressure. It is very hard to imagine this being invented without the theoretical understanding of at least atmospheric pressure, and maybe vacuums. So even if the practical application existed, the 1 AD steam engine couldn't have been able to, say, drain a mine. By the time of the Newcomen engine, other cultures understood atmospheric pressure, and China had at least an example of condensation creating a vacuum, but Ptolemaic Egypt was very very far away from this, and a practical steam engine probably wasn't possible in Europe just from a scientific perspective until the 1600s.
The steam engine is generally considered to be the only invention of the first wave of inventions during the industrial revolution that required knowledge from the ongoing scientific revolution (issues with those names aside), with the rest mostly being the result of tinkering. This doesn't necessarily mean that tinkering earlier could have got you there, for example, a lot of the advances in weaving relied on precision machinery and gears originally developed for watches and clocks. This also happened much later than this time in Egypt.
You can get there to some extent without metal machinery-China had both peddle powered wheels and water-powered frames as early as the late Song or early Yuan. However, the latter couldn't spin cotton due to issues with the short staple length of cotton, which would have drastically altered what any industrial revolution looked like. That said, advances in spinning were clearly not enough, Needham estimates Song's spinning was roughly equivalent to England around 1770-80, as well as a million other inventions.
Instead, the two most important things were shifting to other sources of energy, and the sustained progress since the second industrial revolution that finally moved us past Malthusian conditions pre-industrial society. And in these cases, technological and scientific prerequisites were absolutely critical. I discussed above for the case of the steam engine, but so much of this from the second industrial revolution in chemistry or electronics to more modern advances like computers and air-jet spinning machines and so on are just unimaginable without the scientific prerequisites. China was kinda close to getting a steam engine, but having peddle powered production of cotton and water spun hemp was no where near enough.
A lot of that wasn't discovered for any particular process or industry-the scientific revolution, until the development of industrial research labs in the later half of the 1800s, was a step removed from production. In many cases, discoveries were centuries removed from their applications. When Descartes, Torricelli, Pascal, and so on figured out atmospheric pressure, or von Guericke built the vacuum pump, it wasn't to build a steam engine. Newton and Leibniz's discovery of calculus was not to come up with a theory to describe electromagnetism. Much of the early stages was to learn about the universe and God's place in it, not to create a better fertilizer.
I'm not arguing that development is linear, or that technology and industrialization aren't embedded in society. Tinkering and applications from technicians and artisans still matters as well, even in the 21st century inventions are just a big messy agglomeration of sometimes using applied theory and sometimes just trying things, this is certainly true earlier. Just that the development of the industrial revolution, especially past the early 1800s, isn't predicated on just trade and colonization and tinkering, and science and technology mattered in and of itself. An industrial revolution happen before some sort of scientific revolution was probably impossible.
To get to that, as it developed in Europe, required a mix of Christian universities and intellectual networks, the printing press to facilitate communication and spreading of new ideas, possibly the discovery of the new world to start breaking down resistance to new ideas not contained in the Bible or Greek texts, and more. To get from there to the industrial revolution, you need a broad culture of literacy and ideas that have mechanics and artisans familiar with theory and arguments from literati, and have them able to apply it.
Egypt, and honestly the entire world, during this time, was very very very far from it. The printing press wouldn't start to be discovered until maybe 500ad in China, but really until the Song when it took off, and much later in Europe. Once there, a broad method of inquiry into reality would have to be come up with in some fashion. Furthermore, all of the work in tinkering to build precision engineered parts and weaving and so on would need to be done. Different parts of the world had bits and pieces, but it didn't come together until the industrial revolution. There isn't a ton of agreement about our understanding of a lot of this, and how much earlier or later it is possible to have a scientific revolution looking thing is an impossible to answer counterfactual, but that they weren't close isn't in doubt.
Sources:
This whole argument is fairly Mokyrian (eg. "The Gifts of Athena"), and also draws on reading some discussions on Twitter between Pseudoerasmus, Anton Howes, and others.
The origins of the scientific revolution, and whether it exists at all is also messy and there is a lot of disagreement. I mostly followed a revisionist of revisionist version in "The Invention of Science: A New History of the Scientific Revolution" by Wootton. However, even if you go with some of the more skeptical takes such as in "The Scientific Revolution" by Shapin, I think you need some sort of "network of literati systematically trying things, seeing what reality is, and talking about it with each other", which is probably predicated on printing, at a minimum.
One of the earliest debates on this is the Needham debate, on why it happened in the west before China. The field moved away from that for awhile to argue over whether England or the Yangze delta was marginally wealthier in 1750, but Pomeranz has started to circle back around. In ""Without Coal? Colonies? Calculus?"" he compares existing networks of intelligentsia and how the Kaozheng ("search for evidence") movement in Qing compares to what was happening in Europe. He concludes that they were starting to get there, but were still kinda far and hadn't wrapped in the broader community of artisans and craftsmen you would need to get the "theory driven tinkering" that Europe, and especially England had.
On the broader points around the industrial revolution I'm following the outline in by Pomeranz in the same piece. Written after his "Great Divergence", he acknowledges that his original thesis, while describing the initial divergence, isn't enough to describe what happened after 1850, and potentially not sustained growth. For that, you need the second industrial revolution, which was much more applied science focused. His focus is still on a Europe/China comparison, it matters for the earlier invention of the steam engine when compared with Ptolemaic Egypt.
On the steam engine, there is a chapter in Woottonn that goes in detail. Needham and other's various Science and Civilization in China talks about it in the context of China, as well the parts on weaving.
Needham and Pommeranz think that China had all the pieces for a practical steam engine, but the circumstances to build it were off for various reasons. The collapse of the Song and associated chaos, coal being in the wrong place, networks among the intelligentsia describing but not extending to artisans and craftsman, and so on. I agree with Eric Deng in "Why the Chinese Failed to Develop a Steam Engine" that their understanding of a vacuum was not developed enough for this to be super likely, but they weren't that far off and some of the other factors mattered a lot too.
Finally, there is a broader point here on growth. From Mokyr's "Progress, Useful Knowledge and the Origins of the Industrial Revolution", up to 1800ish Englands growth was Smithian: that is, one off improvements from sources such as increases in trade, colonial extraction, institutional improvements, and so on. What followed was Schumpeterian Growth, based off of relentless technological improvements. That China had weaving technology similar to Europe's at this time and didn't reach Schumpeterian Growth suggests that the initial improvements in weaving cotton are possibly also Smithian, and similar to what happened in the Song dynasty and after would have just been a one off boost, insufficient to lead to the development we've seen since 1800 or so.