Tēnā koe Nikki,
You are right – I totally agree that one of our most significant foundation issues in Aotearoa NZ is access to safe, warm, stable housing. Solving this solves so many other social challenges.
My recommendation is to connect with organisations who are already doing great mahi in this space. The Housing Foundation (https://www.nzhf.org/), Auckland & Wellington City Missions (https://www.aucklandcitymission.org.nz/homeground/) are great places to start. The Salvation Army also puts out some amazing research, especially their State of the Nation report every year. Check out their reports here. https://www.salvationarmy.org.nz/research-policy/social-policy-parliamentary-unit
These organisations may have data sets you can use, or have already conducted research into this complex issue.
I would also recommend thinking about how you may be able to support work already being done, or adapting solutions from one area that might be right for your community, or location that you are interested in supporting. People like Tiny Deane in Rotorua, one of the heroes in addressing homelessness, are great to connect with and learn from.
Work on your problem first to really understand it, then define what solution you beleive (and the people who experience homelessness believe) is the most impactful and then go from there. Setting up a charitable trust comes next, as you need to be sure that that legal structure is the right one for what activity you want to do and importantly the impact you wish to have.
Ngā mihi nui,