The private sector cannot solve unemployment, because it does not control the unemployment rate.
The private sector uses the national government’s currency to affect production and the consumption of that production. Consumer demand comes first, placing pressure on business to increase its production of goods and services from the nation’s finite real resources. The by-product of this interaction is job creation. Business hires more workers to assist it with increased production and to maintain or increase its market share.
If you want the unemployment rate to drop, then the national government must deficit spend for that purpose, introducing more currency into the domestic economy. Doing so relieves the pressure on consumer savings allowing consumers to spend more.
It is the currency-issuing national government that controls the unemployment rate and it is the only entity in existence which can solve unemployment in its domestic economy.