The Greek government hasn’t the financial power to create the kinds of infrastructure programs required, but the rest of the budding Federal European Union does. They must keep the Greek government out of the programs as much as possible because of its history of corruption and its demonstrated incompetence is handling fiscal requirements. Think of a Greater InterEuropean Highway system fully funded, controlled and managed in Brussels using Greek labor and contractors along with projects to modernize port facilities, water conservation and dam facilities, hospitals, schools, etc. within Greece. Billions of over 5 years or less.
The Greek government must be lead to end the internal corruption culture as well as institute strict tax recovery tactics aggressively pursuing and punishing tax evasions and capital flight. Extended debt repayment terms stretching into decades, not forgiveness, are also required.
The Eurozone Monetary Union was set up as a first step to a full political Federal European Union. The Germans and the French, the biggest proponents of such a union, are now in a position take the next step and demonstrate to the rest of the EU members what such a Federal Union can accomplish for the good of the states within such a union.
Right now Deutsche Bank and Chancellor Merkel are strangling both Greece and the hope of a Federal Republic of Europe with the same hand.
I think this would be against EU rules. Much as some may want a federal EU, plenty are opposed to the idea and so we don't actually have one. Brussels can't manage major infrastructre projects directly; these have to be done by providing EU funding to national governments based on proposals submitted by those governments. Changing that would mean a treaty change, which isn't possible, since that would require the consent of 28 governments + 28 parliaments + the electorates of whichever countries are constitutionally obliged, or think it politically expedient, to hold a referendum.