At least in modern blacksmithing there is a lot of mockery for anvils that are not steel which makes me wonder. What did people use before steel? Did they just use iron? Stone? Brass?
In say Octavian/Agustus's time? The 12th-13th centuries?
I'll try to be useful here. I am not sure about really old anvils, what the Egyptians would use for hammering out the edges of their arsenical bronze daggers, circa 3500BC. But steel was known to Greeks and Romans.
When you hear of mockery for people using iron anvils, those anvils are either very high-carbon white cast iron or malleable cast iron. A smith has to not only use the face of an anvil but the edges, for bending, necking down, etc. and old worn anvils typically have very round edges, and neither works particularly well for an anvil- malleable cast iron is soft, white cast iron is brittle. Wrought iron- iron worked until the carbon is burned out of it- is more durable, and a wrought iron anvil is tougher. That would be something the Greeks would be able to use. They would also have been able to face it, weld a top layer of steel, onto a wrought iron anvil as well- though not a 100 kilo anvil like you'd find today. That would have been a pretty big forge for them. Something no more that 40 kilos, perhaps.
EDIT Here's some interesting documentation of medieval anvils that includes not only drawings of excavated ones but one in a medieval drawing. There was a range of sizes. Some look a lot like what a mower would carry and use since at least the 18th c. to peen the edge on a scythe.