Government entities do start up, relative frequently. Every time a new school district opens, or a new library opens, for example. While the scale is clearly quite different, the basics of handling your governing documents (bureaucracy) are the same.
As an example, my town of about 400 does everything a government needs to, with a handful of people meeting once or twice a month, a website, some email addresses, a few Google docs, and a physical town hall to meet in and hold elections. Don't get me wrong, the people who run the town do put in work, but it is far more simple than the state or federal level.
Before you try to build some new solution, I'd research such simple governments and figure out what the minimum needed to operate really is, and where the limit will be as the size scales. Because while the few large government entities are the most obvious and talked about there are literally tens of thousands of small government entities to look at to fully understand the differences of scale in governments.
Look at: Small towns, Library Districts, School Districts, Sanitation Districts, even HOAs.