Japan's version of proof-of-parking (
shako shomeisho) does not require
ownership of a parking space. Permission to
lease the space is good enough. If you are renting in a building with no parking you are not prevented from buying a car. You would just have to find a parking space to lease nearby and prove this to the local police. The policy was imposed in the 1950s in Japan as car-ownership first started to take off. With very narrow residential streets, there was an urgent need to prevent them becoming hopelessly clogged with parked cars. The policy generally succeeded on that goal.
How does one get proof of a parking space? Find the person who is renting (or willing to rent) you a parking space within 2km of where you live and ask for an official document showing that the space is yours. This document is a Certificate of Permission for Use of Parking (hokan basho shodaku shomei) and it must be stamped by the agent. Then go to the local police station and fill out an application form as well as an application form for a badge (hyosho) so you can certify the space. You have to draw two maps in a detailed manner. Paul Barter, assistant professor LKY School of Public Policy | National University of Singapore explains the background more in detail here.
