Depends on your definition of the word since many forms of production are able to co-exist to a certain extent although one form is always the dominant. For instance when Aristoteles wrote "Economics" (in which his definition of what an economy actually is has as a sidenote been extremely influential ever since it was first written and was also the first text in which there was a clear distinction between Use and Exchange values) he made a very clear distinction between the accumulation of capital for the sake of accumulating capital (what he calls Chrematistics) and trading wares to those in need and simply take the price needed to pay for the use-value of the ware and a small administrational fee. This chrematistic art of "making money" is a very early form of capitalism, traders trading wares and consciously "gaming" the trade so as to benefit themselves and acquire power through wealth, but it was far from the dominant form of production of the time.

Throughout the middle ages these "chrematists" slowly kept gaining power and slowly grew in numbers and was slowly became what we now know as the urban class of the third estate. They were far from a homogenous group of people and could be both rich and powerful traders who would later become the capitalist class of the colonial and industrial eras or just skilled workers who were self-employed.

There was however always a conflict between this new class and the already existing dominant class, the feudal lords since the power that the traders gained was subsequently lost from the feudal lords, it was essentially a zero sum game of power which is why the Aristotelean critique of Chrematistics was still very much present at the time.

For a definitive "start" of capitalism you have to either go to the English revolution of 1642-1660 or the French revolution of 1789-1799 where the then fully established urban bourgeoisie finally seized the power over the means of production from the feudal lords.

Source: Marx, Karl. Capital Vol. 1 (1867)