This is one of those classic chicken and egg questions. There can be no exchange without production but production can only happen if there are preceding exchanges.
At first glance it seems that production must be the starting point because if you want to exchange you first have to have produced something to be exchanged. But human productive life is not a series of isolated produce-and-exchange operations. Production is a continuous process, and so is exchange. The exchange of a particular item must come after its production but the terms of the exchange and the means to perform it must be established first, otherwise the production would not take place.
Why does this matter? Is this just a word game?
This question is really about the relative importance of production versus exchange in helping us to understand the evolution of human societies, not so much about which comes first in a temporal sense. Exchange is about the rules of the economic game and the relationships that people enter into in securing their means of life, in much the same way that the rules of football determine how the game of football is played. Football wouldn’t be football as we know it if there were different rules. Change the rules and you end up with a completely different sport, even if the equipment remains more or less the same (e.g. soccer vs rugby, cricket vs baseball, tennis vs hockey).
When put like this it is obvious that the ‘rules’ that govern and the ‘equipment’ that facilitate an activity are more important than the activity itself, in the sense that they define the activity. We cannot say much about how a game will be played if we look only at the equipment and who owns it, yet conventional wisdom has it that the way in which a society produces its means of existence is all important. So much so that human history has been carved up into a series of phases or periods named after the outward appearance of what seem to be distinct economic systems or ‘modes of production’.
We have human beings starting out as scavengers, becoming foragers and then developing various tools and skills to enable them to become hunters and gatherers. Later we have an agrarian revolution where humans learn how to domesticate seeds and animals. This results in a change in the way of living, with humans no longer migrating between food sources or following herds of animals. A more sedentary lifestyle follows, allowing some to specialise in the production of non-essentials and others to manage the storage and distribution of the productive surplus. This led to the formation of highly centralised, distributionist societies, with a mode of production often based on slave labour.
A number of other modes of production have been identified, such as feudalism, mercantilism, industrialism, capitalism, socialism and so forth. Each is contrasted with the others by the outward appearance of the way these societies produced or produce their means of life. Each mode of production is identified by the relationships people entered into, the tools they use/d and
The focus is on production because history preserves artefacts that help us visualise how past societies produced their means of life. Exchange is about relationships, which are more difficult to visualise because the only records are written ones.
Some schools of evolutionary thought consider ownership of the means of production to be crucial. Each stage is defined by the group or class owning and controlling the means of life. Again the focus is on production, this time by competing classes who want to be in charge of production, distribution and hence be in control. This is like saying that a sport is defined by those who own the equipment, fields and stadiums.
Production is also a form of exchange, in that the relations that people enter into to produce something are relationships of exchange. Even in the simplest forms of production, such as a group of hunters going out on a hunt, each participant brings to the task a special skill.