Since the word capitalism lived through many different versions and ideological backrounds, it is relatively hard to project a modern and general idea of capitalism into antiquity.

Roman Empire: Agriculture was the primary factor in production. Many of them were self-sufficient and economized for their own subsistence. The largest part of economy did not work for consumption goods. On the other hand, there were very large agricultural goods in private hands. Older Plinius speaks of six rich landowners which posessed half of the province Africa, so capital accumulation was certainly a thing.

So even though accumulation and private productiongoods existed, it was very differentiated between the very different provinces. On top many smallholders didn't take part in markets.

Central to my understanding of capitalism is a free market, though. A laissez-faire understanding would not fit. Ordoliberalism is the most prominent in my country, so I am going to try it with this understanding.

Protectionism existed, so market access was difficult.It took until Probus that viniculture was allowed in Gaul. Usually sons learned the occupation of their father, it was not their free choice. In late antiquity that was even made a law. Since many of such regulations existed, entrepreneurship was not common. Often times economical strategies were dictated by princeps and municipial aristocraty.

Two central ideas of ordoliberalism are working pricesystem and continouus economical politics.

In the empire money was not only backed up by gold, but the coins itself contained precious metals. In times of much fighting at the north and east borders of the empire, especially combined with usurpations, inflation was heavy. The percent of metal sank and sank, for example during the 3rd century crises, until many people didn't trade with coins anymore. They went back to a barter economy. With that high swings in monetary politics, which could basically change in months because of ongoing usurpations, a capitalistic system had no chance. The stamping workshop were not centralised anymore, many cities had their own. If one usurpator arose, often times he would immediatly stamp his own coins and lower the metal standard, in order to pay a large donativ to the troops. The troops, who created large markets only with their sheer existence, spread the lowered coins. This could go on and on with every new usurpator.

Just curious about some semantics; what definition of "capitalism" would you use? In agricultural societies, I think it's more fair to look at capitalism as a feature as opposed to a defining characteristic of the economy. Although I suppose agrarian imperial economies don't have a word or concept for "capitalism."