Vienna built housing itself, with this housing it was possible to have cheap rents and keep rents from private investors down. https://en.wikipedia.org/wiki/Housing_in_Vienna

Unless you want to build more sprawl-oriented social housing, you'd still need, in most American cities, to reform zoning codes and building codes (single stair and elevator reform) to get Vienna style social housing.

It's a "yes, and" problem though, mostly. Let the market build what it can, and if you want to pursue social housing, do that too - just don't let the perfect be the enemy of the good and delay the reforms while you try and put together all the social housing pieces.

It’s worth noting that a major confounding factor is that, unlike most cities with a housing crisis, Vienna is well below its population peak and so does not need to build nearly as much housing