Left over airplane parts!
Correct. The were fashioned from the cockpit sections of German WWII fighter planes of the same brand. It's another look at German ingenuity.
They had the facilities, the materials, and the technical knowledge and ability to make a product that was ripe for the German market of the post WWII era, they were cheap to build and buy, they were super economical to operate, and were very basic transportation. The exact same technology and mindset that gave us the VW Beetle.
Post WWII Germany was an Occupied country, remember. Also a beaten country. While some of their industrialists were able to survive the war and live pretty high after it, the common German was pretty tight for money, and many had lost their homes. and transportation to the war.
As their civilian economy began to return, many needed transportation to get to/from work. Enter the Messerschmitt. Cheap, economical, easy to get around in, and home built.