To ensure that the Billing System field is filled on every Invoice record, the administrator should make the field universally required. This means that the field will be required on every page layout and record type, regardless of any other settings or conditions.
Creating a Process Builder to set the field or defining an approval process for the child would not necessarily ensure that the field is always filled, as these processes may not run for every record.
Requiring the field on the record type would only apply to records of that specific type, and if the administrator later added a new record type or changed the default record type, the requirement may not be enforced.
Therefore, making the field universally required is the best way to ensure that the requirement is consistently enforced across all Invoice records.