Imho the best policy is to require a permanent parking space close to the main residence of the person owning the car. With permanent access I mean that the space is only to be used for the car and has to be either rented or owned by the person using it. This is rather easy to do in a rural setting, but much harder the more urban the area becomes.
The next part is making access worse for cars. Place parking further away from interesting destinations then bicycle parking and public transport access. Like having bicycle racks right next to the shop doors. That also includes just removing parking as much as possible. Besides handicap spots obviously. Also modal filters to block cars to move through certain streets, but allow bicycles and pedestrians to use those. That can also mean one directional roads.
Slow down cars as much as possible. When cars are as fast as bicycles, cars loose a massive advantage. This has to be done using built infrastructure and not just street signs, but those are an important start. So narrow roads, little viewing space and speed bumps. Also traffic lights are a good option. Give priority to other forms of transport(default green for pedestrians and bicycles for example).
That is exactly my point. Underground parking adds 35-50% to a mid rise building construction cost. That means people have the choice between larger or cheaper units without a parking spot and more expensive ones with a parking spot. Even with underground parking mid rise buildings are already cheaper then single family housing. Especially ifthe area we are talking about has high land prices, like pretty much every city.