A communication POD
Suppose, around 120 AD, an accident of insight occurred in Rome. A plumber, carrying molten lead, spills the lead onto a plaque in the process of being carved. The hardened lead is peeled off and dropped onto wet sand. When cooled, the plumber and carver saw the legible impression and experienced a flash of insight.
Suppose carved words and letters could be arranged and pressed into the wax tablets used for carrying information. There was no paper in Rome and papyrus and parchment was not available for commercial use.
An early form of printing would evolve, first centered on the wax tablets available at the time. Within decades, literacy would improve and so would the supply of people capable of communicating and innovating.
Hero's engine, the quest for printing and the quest for better metals would happen simultaneously. Knowledge and communication would bring innovation. Now, if the Roman empire could remain more stable after the death of Marcus Aurelius, all the better. Expeditions to China could exchange Roman printing and Roman concrete (used to build the Pantheon) for Chinese ironworking and paper manufacture.
There you go. Paper, iron, printing, communication, steam engine. Rome flows into the Renaissance faster than the Huns and Goths can build the forces that took them down.