Did they have enough people to do that?
And as for the 17th century, did anything significant change as far as food production is concerned? The only significant economic activity beyond subsistence farming before the advent of railroads and refrigerators was wool production, and that still requires the first industrial revolution to create demand
Spain definitely had enough people. Portugal was the most prolific colonial power in terms of sending actual colonists until the 1700s, and they only had a population of 1 million compared to Spain's 9 million.
In pre-industrial times, the lower the population density was (in a region fertile enough to support high population density), the higher the standard of living was--so places like England and the Thirteen Colonies had relatively high standards of living, due to rural land providing a surplus of food. This also increased population growth.
In the 17th century food production did evolve somewhat, but it is correct to say that subsistence farming was the main industry even then. However, some areas did produce a grain surplus or wine surplus that was exported to other regions. I believe the Low Countries depended on imported grain.
Argentina could perhaps specialize in naval production, become a recruiting ground for colonial soldiers across the empire, a pastureland to rear horses and trade them across the empire, specialize in the cash crops cotton and rice, or become the main wine production region in the Americas.