Homeless situation....

Some homelessness will not be solved. So, the goal would be to significantly reduce homelessness and provide a path out.

Some parts of the solution would require a culture-wide and city-wide people-level change that is unrealistic, such as never giving cash to panhandlers. As cruel as that sounds, it would go a long way to changing the number of enabled life-style homeless. This has been shown to be the case in many studies (no links for this assertion).

Evangelism leading many (not just homeless) to abandon sinful habits and follow Jesus would make a tremendous difference. (No I am not saying they need to just pick themselves up by the bootstraps, but that a culture-wide revival would certainly change things.) One can look at how drastically things improved in the 1700s when four million out of Britain’s five million people lived in absolute poverty, but as a result of the revival led by John Wesley, within a generation, there was a robust middle class.

Free short-term housing would make a significant difference. The requirements would need to be fleshed out, but a 6-month, twice-renewable housing unit could provide a just the launch needed for someone who is going through a series of unfortunate events.

That's just me brainstorming. I am sure there are other ideas.

Again, homelessness is not something that a single solution will change.