Finland has a housing first policy. The homeless often have multiple problems that prevent them from getting a home the normal way (e.g. drug problems that cause them to get evicted). Instead of insisting people get better while homeless, they’re given homes first and treatment for their other problems after. This coupled with welfare transfers that ensure you never end up homeless just because of lack of money leads to low homeless numbers.

Yes, Finland does this precisely by rejecting Capitalism and giving homeless people homes. This is not a Capitalistic solution.

I get what you're saying, you can have a majority Capitalist society and still solve homelessness, but the answer will never be Capitalism.