Productivity matters to increase real output. Real output will determine the well-being of a country, not running deficits.
Of course the government can create money. Wow, what a great discovery! Nobody had realized that before the MMT sect came along and enlightened us silly mortals! But no matter how much money you create, you cannot guarantee full employment. Because money is just a medium of exchange, not a real resource.
You can create money to pay people to do government jobs ala the Civil Conservation Corps, which increases employment. Nobody can guarantee full employment under any neoliberal system that guarantees and indeed demands unemployment for the purpose of reducing labor value, by the way, so not sure why the hang up on it.