It won't be a government in the Western democratic sense we usually think of. It will maximum be a representative organization aggregated of nation state assemblies that looks very decent, democratic, and established for the well-being of society and the greater good. A senate in times of the Roman Empire, a congregation of unelected officials, who represent yet another ruling group operating in the invisible background. The technology for such a universal control structure to work for long periods of time is now available. The UN structure could be used as a vehicle. The European political structure with its supranational enforcement mechanisms makes it even easier to build already.