Ironically, there's a >50% chance that the solution will entail 1) privately hosted platforms like AWS and 2) privately hosted support services and 3) privately written core modules (McKinsey business strategy, Accenture implemented etc.) and 4) at least some privately contracted IT people to manage the solution.
There's no reason to believe the gov. will make a more robust, scalable and secure solution that other entities.
A better approach might even be to mandate very specific identity protocols, and then allow citizens to chose their own identity provider among those that fit the regulatory requirements and oversight.
For example: https://en.wikipedia.org/wiki/Swiss_Post
It's owned by gov. and effectively independent. They could be an identity provider. They are already close to being able to do whatever need be done.
Having to create new government bureaucracies to do things is hard.