What could've been an earlier date in European History when an Industrial Revolution could have occurred? For example, I remember reading that some French Monasteries, and the Venetian Arsenal have been getting close by the early 1200s towards a standardized proto-assembly line kind of production with water-, animal- and human-powered machines.

Despite there being no real way back then for the construction of advanced water- and steam-powered machinery, and the advanced physics and mathematics of the 18th century not being developed yet, which would lead to efficient engines, the basic principle that "It is better if a human runs in a big hamster-wheel and operates a strike hammer through a pulley-system with precise strikes, rather than he himself trying to strike a nail with his hand-held hammer" was understood by that period.

Was this a possible divergence point for earlier Industrialization in Europe? What are your ideas?
 
There are too many PODs available for this since the Ancient eras. I will try to list out the Ancient and the Medieval era ones as those are what I am interested about.

#1. Ancient Era: Migrations and Urbanization patterns result in a more decentralized and diverse Europe with large cities and city states of diverse origin across Central and Southern Europe. This results in a lack of Slave and Manual laborers. With a steadily increasing prosperity due to trade and contacts and simultaneously develop a Scientific Renaissance. In a couple of Centuries, an Industrial revolution is reached.

#2. Ancient Greeks and Romans: As obvious as it is, a stronger Ancient Graeco-Roman Empire could lead to industrialization happening, instead of a collapse when there was a Slave labor and Soldier shortage.

#3. Carolingian Empire: A strong Carolingian Empire covers massive regions of Central and Western Europe, including Italy and Iberia. As the Empire's effort to build up education and knowledge increase, there's eventually a Scientific Renaissance followed by an Industrial revolution.
 
Avoiding the Plague of Justinian and various burnings of the Great Library (Libraries?) and House of Wisdom would also help.
 
The problem we saw historical plenty of industrialization earlier in history, but they burned themselves out. What made the Industrial Revolution unique was that Scientific Revolution allowed a continue and fast development and improvement in technology. A useful steam engine to drain mines developed in the 13th would only improve very slowly, as artisans experimented and improved, while one developed in the 18th century improved fast thanks to people being able to calculate the needed strength of the materials.
 
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