Is it possible that an apartment block was completely constructed without an allocation of space for management office occupation ? Where to station the management staff for the daily management & admin works ?

Yes, it could happened to any building constructed before the implementations of strata management act (757) 2023. There were residents using the place so call “management office” but it does not belong to common area, it could belongs to developer or anyone’s unit. Please check properly with your strata plan to ensure the allocations of common area.