If the large scale automation involves technology research and Colosseum-sized capital investments like the Industrial Revolution did, you either need the state

If the large scale automation involves technology research and Colosseum-sized capital investments like the Industrial Revolution did, you either need the state or its wealthiest citizens to be interested, or complex financial arrangements for the people that are interested in pursuing that to be able to raise funds A lot of Rome's more ingenious feats of engineering were geared towards military uses or grand public works in the name of Emperors and aristocrats. There wasn't really the same infrastructure for smart engineers that dreamed they could become wealthy from researching and building a new process for making garments at a lower cost (and they were missing lots of intermediate improvements the British had). Ancient Rome had more freedom of thought than, say, modern China, but a lot less entrepreneurial culture.