Get postcode / zip code with Google Geocoding API

Question

I am trying to get the postcode / zip code for the registered users of my platform.

I have access to the following:

1. City Name
2. State ID (Administrative Area Level 1)
3. Country ID (Always Australia)
4. Level 2 ID (Administrative Area Level 2)

I am aware of the Google Geocoding API but I do not have the full address of the user.

Any assistance on this is highly appreciated.