That's the ideal, but a lot of these big problems can't start small because the problem they have is already big. A lot of government IT programs are set up to replace existing software and -processes, often combining a lot of legacy software's jobs and the manual labor involved.

If you have something like a tax office or payroll, they need to integrate decades of legislation and rules. It's doable, but you need to understand the problem (which at those scales is almost impossible to fit in one person's head) and more importantly have diligent processes and architecture to slowly build up and deploy the software.

tl;dr it's hard. I have no experience in anything that scale, I've been at the edges of large organizations (e.g. consumer facing front-ends) for most of my career.