Why one area goes live first and the rest waits
A system that can do everything but nobody uses costs more than none. The first area in production decides whether the project earns trust.

The first area sells the project internally
ERP projects rarely fail on technology and often on acceptance. If the first area runs noticeably better than before, the next one gets a tailwind. If it runs worse, from then on the team defends the old system.
That is why picking the first area is a question of effect, not only of technology.
How to recognise the right first area
It has a clear start and a clear end, few interfaces outward, an owner who carries the topic, and a pain everybody knows. Without that last point there is no motivation to get through the first few weeks.
Bounding it cleanly without isolating it
The first area needs data from around it, even while that surrounding is still in the old system. Those handovers have to be designed deliberately: what gets imported, what gets maintained twice, and for how long.
Open-ended double maintenance is the most common pattern that tips a staged switchover over after all.
How you know it is holding
When nobody opens the old system any more to check a number. That is a better indicator than any formal sign-off, because it cannot be negotiated.
Which area can go first at your company is what the setup check shows, against a real process from your own business.
Setup check