I'm going to talk a bit about the history of the word "capitalism", and about the debates about the economic systems in the ancient world, in terms of your first four criteria, and then a bit about 20th century economies in terms of your last one.  

Markets, money and wage labour

The term "capitalism" was first used in the 19th century, as a label for the existing economic system in the UK and other similar countries.  This was a time when historians and economists talked about "feudualism" as a distinct system of economic organsiation that had covered much of Europe in medieval times. Karl Marx used the term "feudualism" extensively, and contrasted it with capitalism, viewing the two as having very distinct economic systems, with capitalism having replaced feudalism in a revolution where the bourgeois displaced the aristocracy. Marx's intellectual influence has been huge, and many writings in the 20th century, and even now, draw on this conception of there being something distinct about the economic system of the UK of the 18th-20th centuries, compared to earlier times. 

However modern historiography, drawing on research carried out since the 1950s, has a very different view now of economic organisation in medieval Europe. Generally, a lot more complex one that emphases variation between different places and variation in organisation at the same places at different times. In the case of England, the medieval economy is now regarded as highly market-based and accounts of the Industrial Revolution talk more about a gradual change. To quote the economic historian Gregory Clark:

The more we learn about medieval England, the more careful and reflective the scholarship gets, the more prosaic does medieval economic life seem. The story of the medieval economy in some ways seems to be that there is no story.

Back in the bad old days, when the scholarship was less careful, the medieval economy was mysterious and exciting. Marxists, neo-Malthusians, Chayanovians, and other exotics debated vigorously their pet theories of a pre-capitalist economic world in a wild speculative romp. But little by little, as the archives have been systematically explored, and the hypotheses subject to more rigorous examination, medieval economic historians have been retreating from their exotic Eden back to a mundane world alarmingly like our own.

The result of all this research is that we now don't have any agreement of when capitalism came about, and what makes it distinctive, compared to earlier times.

Turning to your definition, involving money, markets and wage labour, we can trace these economic features back much further than medieval England too.  Money, markets and hiring people for wages has a very long history. They were common enough in Biblical times for the authors of the New Testament to use markets as metaphors and parables, for example the Parable of the Workers in the Vineyard (Matthew 20:1-16) uses an analogy of a landowners hiring day labourers for working in his vineyard, the Parable of the Talents (Matthew 25:14-30) uses an analogy of a master expecting his servants to achieve a return on the money he gave them to invest. And we all know the story of Judas betraying Jesus for 30 pieces of silver.

Going back even further in time, the Hekanakhte Papers are a surviving record of Ancient Egyptian economic management from 20th century BCE, so over 4000 years ago. These papers are letters that a landholder and minor priest, Hekanankhte, wrote on a variety of matters, including instructions to the agent managing his land. He discusses grain and cloth sales, renting lands, debts, and the wages to be paid to various servants (apparently in terms of barley). It's not clear whether or not there was coins at this time but Hekanankhte clearly could convert values between different crops or crops versus cloths, which meets a [technical definition of money](https://link.springer.com/referenceworkentry/10.1057/978-1-349-95121-5_2742-1 at least). (Note I am not an Egyptian expert, am about a zillion miles from reading Egyptian hieroglyphs, and am totally relying on secondary literature here). One can argue about how representative Hekanankhte was, but it seems fairly clear that people have been operating in markets for millennia. This is not to say that Ancient Egypt was a solely market economy, there is other evidence of government involvement, but then when is an economy ever purely one thing or another? Even Hong Kong under British rule post-WWII had widespread government ownership of land.

Reinvestment and demand

Your criteria of reinvestment is hard to assess, as so little survives of ordinary people's thoughts for most of history. Ancient cultures saw technological improvements, and often investments in major projects, such as irrigation in Ancient Egypt. Hekanankhte mentions crop rotation, apparently the first mention. And the Parable of the Talents is clearly about seeking an increase in value. 

On your criteria that one should "have demand for this ever increasing production so that one does not run out of demand within one's lifetime", I do not know of any economy that has ever met this criteria. To use the old cliche, there's a shortage of buggy whip manufacturers today. Or, to pick an example from NZ economic history (my own country), the increasing production of wool of the post WWII period eventually outran demand, leading to a fall in sheep numbers. 

This sort of variation is what we would expect, in general. Economic production is set by the intersection of demand and supply, a producer can't ensure demand. Their market might move to a different supplier, or run out of money, or be wiped out by a war or a plague. 

In summary, given your definition, either the development of capitalism is lost in the mists of time, or it has never happened. 

Sources (not given in text).

Ezzamel, Mahmoud. 2002. Accounting for Private Estates and the Household in the Twentieth-Century BC Middle Kingdom, Ancient Egypt. Abacus 38 (2): 235. doi:10.1111/1467-6281.00107.

EH.net reviews of books about the economy in ancient mediterrean states, http://eh.net/?s=ancient+egypt