Probably build a lot of public housing. Plus fix zoning to not make high density housing impractical.

Are we starting from scratch here or working with what capitalism has given us?

This is how my cuntry does it:

1. Make it mandatory for housing developers to build a % of low cost houses for every luxury development at their own cost or not get approval for the luxury development.

2. The government builds high density 3 bedroom apartment complexes that are rent to own for the low income group. These complexes easily house 15,000 people or more.

3. The government subsidises larger terrace houses specifically for young families first house by covering the 10% deposit and tax exemptions.

My cuntry also give free healthcare, schools and subsidised universities.

Giant roof over the whole thing

There are two kinds of homeless people: those who desire shelter, and those who don't. Usually the latter group is in the grip of psychosis, drugs, or both. There needs to be some form of involuntary commitment to deal with them.

For the former group: keep building shelters until there's no more waiting list. There should always be an excess of beds available.

Once that's the case, the only people left on the street are that group I mentioned earlier. But that's a pretty complicated issue to deal with.

I would start with immediate solutions - setting designated areas for camping and providing tents + basic amenities. I'd look into what the most effective policies that exist around the world are and why they work and select the one most applicable to our situation. Finally I'd try and solve the core issue(s) regarding why the majority of those individuals couldn't provide housing for themselves

Public housing. What I am would really make the difference as to what I could do.

If I was a community I would try to acquire property and build the highest density property that made sense and make sure it has a park or land close to it.

Could build a farm next to it to provide jobs and healthy food to the community as well as potential vocational training.

Would focus on getting sane public transit to and from the area. Hopefully after a time private sector would start building up the area and we could locate another area to bring the model to.

Focusing on supply, start encouraging the building of higher density housing, including cheap studio apartments that poor people can afford. This includes changing zoning policies, getting rid of parking minimums, and taxing more of the undeveloped value of land instead of the developed value.

Id kick the speculative investors out of housing. No more leveraging billion dollar hedge fund resources to outbid home buyers driving the price of housing to the moon. No more nimby regulations that prohibit building above a certain number of stories, building certain types of homes or the number of unrelated people living in a house. The only regulations left on the books would directly tackle legitimate safety concerns and thats it. Id make it as easy as possible to upgrade or build new housing while enforcing the regulations necessary for housing to be safe to live in. Id encourage the formation of cooperative housing i.e the people living in a complex are part owners and so the management of that building is incentivized not to screw them over. Id dump money into public housing and bolster the occupants' ability to take care of themselves with job training, education and support they need to dig their way out of poverty.

In my own city, with an unlimited budget?

Take 1/3 the office buildings and make them housing. That gives us the density we need inside the city. Keep going, we do have enough space here. Keep going until rent and housing cost drops to be more in line with wages. Restore transit so that transportation cost is not such an enormous expense (where I am, 2 cars can easily cost $1k a month, say one car payment, insurance x2, and gas and maintenance) so people in this more tightly defined space didn't need cars so desperately.

(ETA: I would also buy back the electric company from the out-of-country conglomerate that bought it & create a cheap city fiber optic internet service. Do the things that cost up front then reduce everyone's cost over time. We already have city run water & garbage)

Then would need to tackle the actual homeless - are you saying we'd need to house even people who do not want an indoor space? People who will never have a job and don't want to be part of the system? This is a small but non-zero number. For those I think more widely distributed facilities at every single park in the city, well maintained and clean, so it would not be so terrible trying to just get a shower. And lots of outreach to get those who do want a place, into a place, and the help they need to have a good enough life.

Make house scalping illegal. Aka no rented homes.

Deport everyone without a house? Very obviously?

(obviously a /s)

1. Individuals can own a maximum of two properties.
2. Corporations can own a maximum of X rental properties (enough to allow a dedicated team to find a career servicing them, maintaining them, etc but not many past that point - I'd like wager in the low single digits).

This discourages using housing as a financial asset past owning where you live. This alone should reduce the cost of housing significantly. Housing gets cheaper, more people have housing.

3. Create programs where people or cities can get stable, low cost loans from the government to construct housing ranging from detached single family homes to high density apartment complexes.

4. If you live somewhere with restrictive zoning laws, revise them for the modern age.

This should allow communities to solve their own housing issues via lowering the financial burden of various solutions.

5. Continue to offer free shelter for homeless who want it and need a place to get back on their feet, provide amenities that make that transition easier.

6. Create a research task force to determine any other causes of homelessness and propose solutions. I'd wager: legalizing most drugs, forced mental rehabilitation, and sunset laws for criminal records would get rid of the rest.

Campground with three-walled shelters with twin bunk beds around the perimeter. It should also have potable water, electrical outlets, flush toilets, hot showers, laundry, and trash service. The showers and laundry could be funded by dollar coins. Any resident or camper can earn dollar coins (no paperwork required), by doing work (litter collection, landscaping, cleaning bathrooms, roll call, etc). There should also be lockers to secure belongings. It should be near transit and with plenty of secure bicycle parking.

Build very basic shelters wherever land is cheap. They will have tiny private rooms with locking doors, and if people want to use drugs in there, fine. Tax land values severely enough that speculation is no longer a good source of income. Allow people to build more housing.

Tree houses for all!

Housing with 1 to 3 doors meant for renting can be owned by regular people only, 4 to 8 doors for rent must be owned by a corporation (with the financial implications), any more then that is owned by a non profit crown corporation. That doesn't prevent condos from existing.

All properties come with a 50km radius in which people can't own a second property. That means you can't buy a house and have a rental property in the same city, it also means if you own a multi units building you must live in it.

Have the previously mentioned crown corporation buy/seize lots (especially unused lots) to build more high density buildings with cheap rent.

Increase taxes on single family housing based on the size of the lot it's built on. Want to own a single family house on a lot big enough for two houses? Pay the taxes for two houses.

And all the normal stuff, public transport, parks, homeless shelters, social services.......