Oh my friend, you have some reading to do!
The capitalist market system is really only a few hundred years old! If you believe Meiksins Wood, she puts it at about the mid 1700s, others put it a little later.
And even then, it took quite some time to reach the rest of the globe.
We've had non-capitalist market economies, anarchist economies, communist economies (of various flavors), gift economies, and many other ways of organizing people.
Ask the folks who run Food Not Bombs about whether they are 'organized by the market'. :D