Early democratic projects
Early steam engines
The industrial revolution began with the invention of productive steam engines in the 18th century. However, precursors to those engines existed as early as the 1st century. Even though those machines were not exactly fit for productive application, it seems plausible that the necessary technological progress could have been made relatively quickly. Why didn't that happen, then? Most probably because of social reasons.
Democracy kills cheap labor
Engineers of ancient Rome knew of the Aeolipile, and would have had the knowledge and resources to make it production-ready. However, they were quite busy with designing military applications and infrastructure, as well as bringing water to the sizeable (and growing) population of Rome. Additionally, there was simply no need, because Rome's economy was based on slave labor, which was exceedingly cheap.
A medium article states:
The missing component, perhaps, was the will [emphasis in original] to find a source of greater power than what was offered by domesticated animals, the wind or water streams. The Roman world was a slave economy, employing abundant and cheap muscle power provided by human captives. Practically none of the great thinkers of the classical age, no matter how thought out their perspectives on other ethical issues, dared question the legitimacy of slavery.
Now, if we could remove slave labor from that environment, the pressure to find a technological replacement should further the development of steam engines quickly and drastically. How do we do that?
The easiest way seems to lie in early democratic movements, providing certain protections and liberties to the common people. For the time period you want, an obvious candidate is the Magna Carta, which was signed in 1215. We know now that it still took several hundred years for democracy to be established in Europe, but it the ideas were there, and therefore history could have gone differently (I don't know if you would like to describe that process in any detail, in the worst case you could probably just handwave it, as it is often done in alternative-timeline stories).
As Philipp pointed out in the comments, it should be noted the economy in the middle ages is not slave-based as it was in ancient Rome, but it is based on a very similar system of servitude. This is what I based my reasoning on, but I failed to make it explicit, before.
If you already have a strong democracy established, the industrial revolution will certainly look differently than the one in our universe (consider the social impact as well as criticism leveled against industrialization), so if you want to keep it similar, the democratic project must not be too succesfull (enough to prevent slavery, but not enough to prevent huge gaps in wealth and power between owners and workers).
This is of course not too far from what happened in England in the 18th century: Even though steam engines were more expensive and less powerful than water mills for quite some time, they allowed the building and operation of factories in densely populated areas, independently from any rivers. So if you want to go down that road, our own history might just give you what you need.