We also have to be realistic and understand that whatever we do is going to be insanely expensive and in the very best case take years to improve the situation. That doesn't mean we shouldn't start but when people start screaming about how expensive it is we need to remember what we are signing up for.
There isn't going to be one solution, largely because there are some distinct populations of homeless folks and they'll need different kinds of help.
People who are working or are able to work should be given generous help to get housed, employed, and keep them working. That's probably a third of the homeless population and the easiest win to take. It still won't be cheap. Just not as ruinously expensive as what will come next...
People with a drug addiction should be given treatment and temporary housing. Then hopefully they can transition to the first category. Addiction treatment isn't 100 percent effective and is insanely expensive, on the order of $50,000 per patient. This is approximately the cost of a first-class summer vacation to Italy, and I suspect will be about as politically popular as giving all our heroin addicts free Italian vacations. There is also a capacity issue because we don't have enough treatment beds to treat everyone, and a homeless drug addict on a waiting list is still homeless and still on the streets.
People with mental health issues should again be given treatment and temporary housing. But again mental health "treatment" is at best primitive (approximately where medical care was when it was practiced with leeches) and not always effective. But it is still enormously expensive and again spending that much money on homeless people won't be politically popular. And again we don't have the number of mental health professionals needed to treat all of these people, even ineffectively. So we'll need to train them (mental health professionals) before we can make a real dent in this problem.
Finally, there will be some people we can't treat and can't help in any polite way. We're going to have to man up and admit that and also have the strong stomach it will take to involuntarily detain those people (some are criminals hiding amongst the homeless population, so involuntary detention will be prison) where they won't be a danger to themselves or others. This will involve bringing back involuntary commitment for the mentally ill and probably also "vagrancy" laws (even though those laws had a pretty toxic history).
I just have to question whether we will ever be willing to pay what all this will cost.