POD is 121 AD. A fountain is under construction in Rome. A stone carver is doing a plaque. A plumber accidentally spills molten lead on to the carved stone. They lift the hardened lead off the stone and, because it is still hot, drop it face down on to a bed of damp sand.
They lift the lead off the sand and see the legible inscription left by the lead. The carver feels a Gutenberg-like flash of insight and cuts the lead into words and prints images in to the sand. Three senators walk by and see the accidental demonstration and recognize the technique can be used as a tool for communication. They take the pieces of lead to Emperor Hadrian.
Hadrian commissions jewelers to carve letters and words that can be pressed into the wax tablets in use at the time (no paper back then). Texts and messages could be quickly spread without the labor of manual copy. Early day kiosks spread news. School lessons are handed out faster. Libraries spring up.
It would be decades before Rome would feel the instability that followed the death of Marcus Aurelius. In the meantime, literacy could spread. Roman Latin becomes even more widespread and standardized. More literacy means more people available for invention.
I am no expert at Roman history. The challenge is to continue this scenario so Rome becomes too strong to fall, perhaps aided by a cultural/technological exchange with China in a future century. Effectively, China plus Rome equals Renaissance.
This is a very interesting concept. One that I very much like.
I must say that the fact you made it Emperor Hadrian is a good thing. Considering that the Empire was still strong during his time it provides for a nice basis for the continued development of strength.
Another major facet of this is that it becomes slightly easier to standardize training for various facets. Such as the military - you give every squadron a Book of Rules or whatever which can help to make them better trained.
Another facet is that now laws can be published and handed out to everybody in a way that makes it so that everybody knows what is and what is not possible.
Of course, there is the spreading of news and information. And that always helps.
The spreading of information would allow for the existence of magazines about various topics. Think about it, a magazine related to mining, or agriculture. And if a dozen rich and powerful mining experts are a part of the mining magazine then they can exchange ideas in print. Providing for an increased in development.
Books and magazines would convey knowledge, but only with the help of papyrus (from the Nile) or paper (just invented in China and not yet in Rome). After some decades, we can assume books and literature would be spread in Latin and Greek. Wax tablets would have to suffice for news bulletins, since the supply of papyrus would be limited.
In 125 AD OTL, the Pantheon was built of concrete construction. The fired ingredients came from volcanic sources. Unfortunately, in OTL, the technology was not properly recorded and was eventually lost. With education and literature, the technology would be recorded.
I chose the POD point to assure that Marcus Aurelius would be born exactly as in OTL, so Rome would remain stable through 180 AD.
Statistics say that Rome was, at best 30% literate at its height. I want to spread education to double that number by the end of the second century, so essentially twice as many people would be able to innovate and contribute. Hopefully, the instability that followed the death of Marcus Aurelius could be reduced.
Ultimately, I would like to see an expedition from Rome to China in the third century. I would suggest a sea route, around India and southeast Asia. This means a stable Roman base in the Suez or Persian Gulf.
A technological exchange between China and Rome would change the world. The empires would be too far apart to fight. Imagine: Roman printing and concrete for Chinese paper and iron technology. We can not neglect the impact of an exchange of medical and martial art techniques.
I will stop for now and see if anyone else has some suggestions.