We've actually had similar issues in many post-war suburbs in Germany when trying to convert them to transit in recent years.
The solution isn't to remove all driving, just driving in areas with too much traffic. So park & ride concepts were created. You build train stations at major hubs and at locations at the edge of town and connect them.
e.g. my mum's commute changed from "drive for 45min in traffic" to "drive 5min to the neighborhood train station that shares its parking lot with the hypermarket next door, wait 10min, ride the train for 5min, arrive at the train station next to her office".
Her commute was cut in half, the business can collect revenue from their mostly unused parking lot during the week (it's sized for saturday shopping traffic), the train station doesn't have to build their own parking lot (the operator pays a few cents per train ticket to the business), and every person using this line is one less car on the road.
This model is already profitable (!), but you can expand further.
You can set up bus or tram routes that offer cross-connections between train stations to further connect schools, university dorms, malls, etc.
You can then improve connectivity within of suburbs. Introduce cross-connections between cul-de-sacs for pedestrians and cyclists, connecting suburbs, apartment complexes, local businesses and train stations.
The density won't be high enough to make walking to the train station viable, but cycling to the station certainly will be. That's not a solution for everyone, but it increases freedom of movement for teenagers and retirees.
So far, all of this is possible in the US today.
But we can dream beyond that:
You'd really want to change the zoning around these hubs over time.
Ideally you'd want to build 5-over-1s with an underground parking garage, shops and stores on the bottom floor, and apartments on the higher floors.
For businesses that need more space you can give the bottom floor a larger footprint and add a green roof which provides something of a community backyard for the occupants of the apartments. Bonus points if you build it as a courtyard in the middle with balconies facing the courtyard.
You'd really want to avoid high rises to ensure you get a growing circle of mid-density development around these hubs, somewhat reminescent of what main streets used to look like (or Disney's Main Street USA with two more floors ontop).
A few cities in the US have actually gotten this far already!
European cities, which suffered more destruction from post-war car-centric city planners than from the war itself, have been using these steps to slowly recover.
These steps are also how cities around the world grew during the industrialization, and how the US got the main streets of old in the first place.
Getting this far will take a whole generation, but where do we go from here?
While this would be the end for solving local commuters, it'd only be the beginning for inter-city journeys.
HSR is 2×-3× faster than cars and can be faster than flying for journeys below 1500-2000km, but it only works if you've already got local hubs with a dense transit network connecting them to the rest of the city.