Seems like an absurd question, actually. They didn't have the technology, the cohesion, the population density nor the sources.
# Agrarian society, with nothing to do during winter months, leading to home businesses.
Over the centuries agriculture had improved a lot. The Commercial Revolution (starting in the 14th century up to the 18th century until the Industrial Age) took off in Europe, because farmers were able to produce far more per square acre and because they were getting increasingly free from their aristocratic landlords. Thus, farmers were able to produce a surplus of agricultural resources and sell them.
Before a society can even make a transfer from the one sector to the next (agriculture to industrial), there should at least be a significant portion of the society capable of occupying themselves with other jobs. The Commerical Revolution brought (though not immediately), for the first time since the neolithic revolution, a society not based primarily on agriculture.
This, in turn, created an increasingly powerful middle-class which directly stimulated investments, etcetera. It was the beginning of capitalism and also the beginning not of a town-centered economy, but a nation-centered economy.
# Urbanization
I think urbanization is rather a consequence of industrialization than a cause. Factories were built in the cities, thus creating jobs there. Besides, the Roman Empire may be impressive in size, but it was still an empire primarily based on agriculture and it wasn't that cohesive. Historians believe people living on the periphery were probably not even aware that they were living in such a giant empire.
# Banking system
I don't really want to go into this too much, but banking, stocks and those kind of phenomena were only really developing after the middle ages. Banks were operating on a western European scale, had great authority and the system in itself was becoming more involved in the European economies as capital was drawn from the colonies overzeas and increasing wealth was used to invest, thus take out loans, etc.
Also, if I remember correctly, in Rome there was rather a kind of patron-system instead of an all-encompassing banking mechanism. People loaned from aristocrats and they paid them back in labor or even sometimes sold their children.
# Stability
What do you exactly mean with this? I think most societies are stable for most of the time.
# Large amount of capital
As I explained above, wealth came from the colonies, investors, a nation-based economy, free trade, more cohesion, a wealthier middle-class, etcetera.
# Relative free market
The word 'market' isn't a good word for describing the economy at that point, in my view. There were some things sold here and there, but peasants produced little or no surplus. Merchants were present of course, but one cannot speak of a market economy. The first market economy in the world was beginning to emerge in China around the tenth century or so, but before that there was no known civilization running an economy driven by overall supply and demand.
# Population growth
Population growth is again something which is almost always going on in a society. The question is at what level? There wasn't as much population density at that time of course. There were as much as 40-60 million people living in the Roman Empire at its territorial maximum while around 1800 Europe had a population of about 200 million people.
Besides the numbers itself, it were the economic and scientific conditions of Europe which steered this population growth in the direction it needed to be to maintain itself with the help of the rise of the market economy.
# Vast empires, and access to natural resources
There are tons of reasons why the commercial trade-post empires and the Spanish empire created more wealth for Europe while the Romans, which were after all as a society in an incredible amount of aspects less advanced, didn't have all of that. They did maintain commercial relations with Asia and Africa, but not on the scale or level as the Europeans did later on.