For how long should a ventilation system be operated for a new facility?

Answer 1

The amount of time depends on the reason the building is being ventilated. You need to be more specific with details in order to make this a question to which we can send answers.

Answer 2

Local Building Codes usually have requirements for HVAC systems to provide sufficient ventillation in order to supply a minimum number of total air changes per hour within any given structure, depending on the use and function of the building....a manufacturing facility would require more air changes than an office building, etc.
The ventillation systems are then programmed and set up to provide the required air changes automatically (ideally).
In order to answer the question, the type of building and the activities that were performed within the building would have to be known.