There are strategies to remove cars and you can make effectively car free suburbs, but I'm not sure you can make an entirely car free city. The biggest issue is trucks, everything needs to be planned around getting trucks out of the places everyone else is driving.

The other strategy is getting everyone onto bikes and onto public transport. If they can do it, citizens will prioritize public transport and cycling over cars. So once you get rid of the trucks, and design the city in such a way that citizens can cycle/train to work/commercial then you'll reduce heaps of traffic.

Interestingly, I built high speed rail to a second town I built that's only connection is the railway, it's quite small but also very little traffic. Almost everyone takes the rail into the main city for work. I think better cities in the game would actually be to treat suburbs like a series of small towns, rather than lots of massive city blocks.