What do you mean by “mass production”? Do you mean mechanization or simply organized enterprises that produced some commodity in large quantities? Because if it’s the latter, then I would point to chicken farming as one such enterprise.

Romans loved chicken and their chicken farms were huge, producing both eggs and meat. When I say “huge” I’m talking tens of thousands of birds in some cases. There are many treatises on chicken farming from Roman times that describe it in great detail. Lucius Columella lived around 70 AD and wrote profusely on agriculture, including chicken farming at his own estates at Alba, Carseoli and Ardea. He describes the different breeds of chickens on his farms, the virtues and vices of each, how to house them, what to feed them, how to increase egg output, when to slaughter the hens as they grow older and lay fewer eggs. This was very much farming on an industrial scale. An even earlier account is from Marcus Terentius Varro in Rerum Rusticarum Libri III (Agricultural topics in 3 volumes) from around the time of Caesar. He wrote a bunch of other agricultural books too, which have now been lost but survive in parts quoted by Cato and Pliny.

For that matter, chicken farming as in “mass production” goes back even earlier to ancient Egypt, where they discovered how to artificially incubate chicken eggs to create these large chicken farms, a technique that the Romans learned from them. Chicken eggs need to be incubated in very particular conditions – at a temperature of 99-105 F, with a relative humidity of 55%, which must be increased close to the end. The eggs have to be turned over every few days, or they’ll hatch into deformed chicks.

The ancient Egyptians built complexes of chambers, connected by passages and all fed centrally with heated air from big furnaces outside, fueled by straw and dung. These were large scale operations with dozens of incubation chambers, supervised by chicken experts and staffed with attendants to turn over the eggs periodically. They produced huge flocks of chickens on a scale that I’d definitely call “mass production”.

If you mean mass production as in factories manufacturing goods on a large scale, I don’t know, perhaps someone else could comment.

They did have very large and extensive mining operations throughout the empire. One of the best known sites is the gold mines at Las Medulas in Spain, where Roman miners engaged in ruina montium, a form of strip mining. Pliny wrote about it in chapter 33 of the Naturalis Historia