Shininess isn’t an indicator of whether or not something is made of iron or steel. Most Roman armor from the late Republican and the Imperial periods was made of iron. It isn’t until the early medieval period and the creation of blast furnaces that large-scale steel production for armor is really viable.

The “plate armor” you’re referring to is the so-called lorica segmentata (this name actually dates from the 1500s and we don’t know what the Romans called this style of armor). Lorica being “armor” in Latin, and segmentata meaning “segmented,” for the banded construction. Its use dates from just before the 1st century AD to around the 3rd century AD, the period we’d think of as the height of the Roman Empire.

Some of this style of Roman armor was part-steel. A fragment of a lorcia segmentata found at the Vindolanda fort south of Hadrian’s Wall in England is part-iron, part-steel. The inside of the armor is softer wrought iron. The outside is harder mild steel. The steel was made by taking iron and wrapping it with organic material. This was then wrapped in organic material and heated in a forge, transferring some of the carbon into the iron. Today, we’d refer to this technique as case-hardening. The iron and steel pieces were then welded together, creating a laminated metal strip. Similar steel-iron laminating techniques were used to build Roman hand tools like knives and axes. But these steel armor examples are fairly rare, and iron seems to have been the primary material used to make armor.

As for the point about mass-production, here’s some context. Prior to the Marian Reforms in 107 BC, then-Republican Rome didn't have a professional military. Instead, private citizens were expected to provide their own weapons and armor when called up (or asked to volunteer) for military service. Since arms and weapons were made by individual craftsmen, they were quite pricey, so limited military service mostly to the lower-middle, middle and upper classes. This leads to very visible social divisions with the legion itself. The manipular legion is divided into three main lines of infantry, with the younger, less-prosperous hastati in the front line and the older, richer, and better-armed triarii at the rear as a reserve. The poorest men fought as unarmored skirmishing velites and the richest men fought as equites, mounted on their expensive horses.

Gaius Marius, then the junior consul, shakes this system up. In 107 BC, Rome is fighting two wars: one Transalpine Gaul (i.e. the French Riveria) and one in North African against the Numidians. Marius needs more troops to fight in Africa, so he persuades the Roman government to let lower-class Roman citizens join the army. Since lower-class recruits obviously can't pay for their own equipment, the government has to provide them with weapons and armor (at the time, the lorcia segmentata hadn't been invented, so it wouldn't have been issued). It's almost certain wealthier citizens doing the military service would have still bought their own armor and weapons.

The Marian reforms also reshape the Roman legion. Gone is the three-lined manipular legion. Instead, the legion is divided into ten cohorts, each with six centuries with 80 fighting men (yep, only 80 legionaries in a century, but there are 20 servants in the century, making it a round 100 men). This basic organization would remain in place until nearly the end of the Empire.

The Marian Reforms essentially create a (partially) state-armed Roman army. The basic organization of the Marian-era legion, the growing professionalism, and the practice of more universal recruitment become important characteristics of the later republican and imperial legion. This also means the government of the Roman Republic has to start producing and procuring armor on an even large scale. When Rome becomes an empire and continues its aggressive expansion, the demand for weapons and armor only grows. So, how to meet this demand?

Continued...

e: some edits for clarity.