The short answer is that there are scholars who consider these places to be capitalist: Braudel called 13th century Florence capitalist, and quite famously Max Weber argued for the existence of "ancient capitalism" in Rome and China.

It all boils down to what one means by capitalism. "Capitalism" is a remarkably elastic term that means a variety of things to different authors. Braudel, for example, focuses on long-distance trade and commerce, and consequently finds "that capitalism has been potentially visible since the dawn of history, and that it has developed and perpetuated itself down the ages." Likewise, Weber defined capitalism primarily in terms of rationally calculated profit-seeking behavior. The Cambridge History of Capitalism, which I think is fairly representative of mainstream economic historians, defines capitalism in terms of four elements:

1. private property rights
2. contracts enforceable by third parties
3. markets with responsive prices
4. supportive governments

Defined in this way, capitalism would seem to exist basically anywhere a relatively free market exists, and unsurprisingly the authors find examples of capitalism going back to antiquity. If one defines capitalism in terms of the existence of private property and the pervasive operation of markets, then one can find capitalism virtually anywhere. Even definitions of capitalism that focus on markets in land and labor, for instance, have to contend with the fact that these are very widespread phenomenon: the economic historian Bas van Bavel, for instance, has found evidence of widespread labor markets in ancient Mesopotamia (cf. his An Invisible Hand?).

So there are historians, both old and new, who would argue that capitalism pre-dates the 16th century.

There are also historians who tend argue the opposite, that capitalism is fundamentally modern. Generally speaking, these historians tend to be of a Marxist or marxisant orientation. They tend to define capitalism in narrower terms, focusing on the relations people form in the process of production. For example, the economic historian and Marxist Robert Brenner argues that capitalist "social-property relations" only prevail where the following is true:

1. Economic agents must be separated from their means of subsistence. Though they may possess means of production - tools and skills - the individual economic agents cannot possess their full means of subsistence, i.e. all that is necessary to allow them to directly produce what they need to survive. What this usually means is that, at minimum, they must be deprived of ownership of land [...]
2. Economic agents must lack means of coercion that would allow them to reproduce themselves by systematically appropriating by force what they would need from direct producers.

Brenner is quite famous for arguing that these conditions generally did not hold true anywhere in the world prior to England in the late 15th/early 16th century. This sparked a controversy known as the "Brenner Debate" among both Marxist and non-Marxist historians. Even within the Marxist tradition, however, there are disagreements over what exactly constitutes "capitalism." The late antique Marxist historian Jairus Banaji, for instance, has also argued that elements of capitalism existed in ancient Rome.

Ultimately there isn't a definitive answer to your question because there is no definitive definition of capitalism that all scholars use. It only makes sense to ask this question with respect to a specific definition. For the authors of the Cambridge History of Capitalism, both Florence and Rome have elements of capitalism, if not capitalism itself; for someone like Brenner, these are societies that lack the specific characteristics of capitalist production. At the end of the day it depends on who you are asking.

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Fernand Braudel, Capitalism and Civilization

Larry Neal & Jeffrey Williamson (eds), The Cambridge History of Capitalism, vol I

Robert Brenner, "Property and Progress," in Marxist History-Writing for the Twenty-First Century

Jairus Banaji, Exploring the Economy of Late Antiquity

Hi,

While you wait for an answer, you may be interested in the following previously answered question:

• Was Joseph Schumpeter right in saying that Capitalism began in Medieval Italian cities like Florence during Renaissance? Answered by /u/AlviseFalier

The replies to this answer are also very much worth reading, as they go into a lot more detail on this argument.

Just to add a bit to what has already been said, the dependency theorist Andre Gunder Frank, along with his collaborator Barry Gills, has argued that there has only been one "world-system" of commerce ever, that this system is approximately 5,000 years old, that its core is southeastern and central China, and that it has in effect been capitalist from the outset.

Gunder Frank was working off of the global history of capitalism advanced by scholars like Braudel and Immanuel Wallerstein and Eric Wolf and work like Janet Abu-Lughod's Before European Hegemony, which argued that there was a "world-system" of commerce that not only preceded modern Western capitalism but within which the West was something of an underdeveloped periphery, with South Asia and East Asia (specifically southeastern China) being the core or metropole of the world system between 300-1400 CE.

Gunder Frank argues that most production in local and regional economies was about the production of food and basic household items like clothing, oil for lighting, pottery for food storage, simple furniture and the like. A few commodities were produced for regional trade, often at the boundaries of distinct ecosystems, goods that were too bulky or not sufficiently distinctive to be worth transporting very long distances but which would be valued for their distinctive novelty or properties in neighboring regions. (Say, particular hides or furs, grain or durable dried foodstuffs, etc.) These kinds of exchanges were mostly barter or involved exchanging services.

But the kinds of commodities which had unusual value all around the existing societies of Eurasia and Africa and which were light and small enough to be transportable over very long distances, according to Gunder Frank, required some degree of systematizing of global commerce and some recognized standards for currencies and equivalencies, with silver in use in China being the most important to determining stable values across the whole of the premodern world-system--and generating shared institutions like banks, credit and taxation in a way that he argued was basically capitalist in nature. Post-1400 European capitalism, in Gunder Frank's view late in his career was both a massive elaboration of this very ancient core system and an aberration that vaulted a former periphery into dominance for a finite number of centuries. (Late in life, Gunder Frank argued that the 'center' of the world-system would naturally revert to China in the 21st Century.)

Most historians are disinclined to accept this characterization simply because with our varying regional and temporal expertise we can see a great many ways in which the premodern (and indeed, the modern) "world-system(s)" are not very systemic, or have relatively little penetration into and influence over the localities we study. Or we are also inclined to stress the relative novelty and specificity of the institutions we study most closely--thinking for example of the specificity of changes in banking and credit in Genoa and other Italian city-states in the early modern era, or of the institutional distinctiveness of global-scale trading companies like the Dutch East India Company, or simply about the infrastructures necessary for the massive expansion of volume and impact of global trade after 1500. It seems hard for me to say that the relatively small amounts of gold and ivory being produced out of interior southern Africa in 1300 by Shona-speaking states that were traded in a long series of middleman transactions to South Asia and East Asia, with some ceramics and fabric finding their way back to southern Africa is "capitalism" in the same way that the industrial production of a broad range of commodities for mass consumption in southern Africa today is.

By that standard, there also have only been two or three kinds of human political systems and they're all effectively the same from 400 CE to today, two or three basic patterns of human life and they're all the same. Historians are focused on change-over-time, so we're not very friendly to arguments that nothing much has changed. There are other reasons to challenge Gunder Frank--many of his fellow Marxist scholars working on world-systems theory have pointedly disagreed with this interpretations, for example. But still, it's a good challenge and it gets at what the OP is asking: precisely what is it that distinguishes capitalism from other systems of commerce in world history? If it turns out that most of what we regard as distinguishing features of capitalism have considerable antiquity, then maybe capitalism is not so much as distinction of type as it is a distinction in scale and consequential power, e.g., after 1500, commercial systems that applied only to a small amount of global trade which affected only powerful and wealthy elites begin to infiltrate all aspects of economic life and all forms of exchange.