No. Offer actual affordable housing. New housing has more than doubled in size since the 1950s, plus we have largely eliminated small, cheap housing alternatives, such as SROs* and boarding houses. There is no end to how much we can grow houses and inflate the cost associated with not being homeless. If we don't deal with housing, no amount of raising wages fixes this problem.
Though I agree that we need to provide universal health care.
Additionally if the unemployment is 4% then raising it slightly isn't a problem. 0% unemployment is bad for an economy and the US has safely hovered between 4-6% which is needed to let businesses be able to hire when more workers are needed
Not that it won't happen soon anyway, but why hasten it.