We also need to be careful about what we build - it can't just be more SFH.
The ideal would be for municipally owned mid-rise apartments in mixed-use neighborhoods to become common. Vienna does this very well, but public housing has been demonized in America (and, like the lazy dad who does a chore so badly they never get asked to do it again, our federal government starved public housing support so badly that most Americans think of it as an intrinsically horrific way to live).
Just allowing the type of housing you describe to be built by anyone would probably go a long way. I think another key ingredients is smoothing out and accelerating the permitting process. Shutting down hyper-local input that drags everything out is also a must. Someone wanted to convert a bunch of SFHs across the street from me into exactly what you describe and community protests shut it down. Happens all the time. People just hate change when it's near them.
I understand that in Japan there is a set of federally defined zoning types. Some beaurocrat checks your proposal against the requirements of the zone you want to build in and you get your permit or rejection within days. It's difficult to comprehend the massive impact it would have for permitting to go from an expensive, multi-year dice roll to a mostly predictable process that takes days.
The ideal would be for municipally owned mid-rise apartments in mixed-use neighborhoods to become common. Vienna does this very well, but public housing has been demonized in America (and, like the lazy dad who does a chore so badly they never get asked to do it again, our federal government starved public housing support so badly that most Americans think of it as an intrinsically horrific way to live).