The playbook for building massive amounts of housing at affordable prices exists already, you can copy basically everything Sweden did in their project Miljonprogrammet.
- The government funds construction of the housing. Large buyer = big leverage to get costs down in contract negotiations
- Build apartment buildings. Sharing walls with neighbours = lower cost per unit of housing
- Standardize the building designs. Less customization = lower costs
- Pre-build modules and assemble on-site. Factory construction = lower costs
With the density afforded by this construction pattern it also makes lots of sense to build great transit in connection with the area, and some retail nearby/in the same building. This further improves the overall efficiency of the area