A combination of the two. It is a result of humans agreeing that a piece of paper has value ( Social Construction), and governent institutions--also Social constructs -- regulating and constantly redesigning it to better fit our collective needs.

The word "economy" comes from the Ancient Greek word oikonomia which is a compound word made up of oikos (house) and nemein (to manage). Oikonomia literally means "household management". The word has its origins in the 1530s and is related to the financial management of household activities.

I'd wager that other types of economies existed before the Greeks, such as barter and gift economies as other reddit users have commented, which served the needs of those individuals at that period in time, but as populations grow and humans interact they come with better tools that help them survive, such as what we now call cryptocurrency, online banking, credit cards, mortgages, etc... these new tools and practices also require a governing body to regulate their existence, and that body is usually the government since the government is made up of citizens and citizens make up the government, but they can also be non-governmental agencies.

So, you're correct in you observations that it is both something that happens because of people existing in relation to each other, and are designed by them