You can make a smart campaign that is either triggered or scheduled and write the value with lead tokens!
Smart List
Trigger: Lead is created
Filter #1: Postal Code is Empty
Filter #2: Inferred Postal Code is not Empty
Flow
Flow Step #1: Change Data Value: Postal Code. New value = {{lead.Inferred Postal Code}}
That will populate your field (assuming it's called "Postal Code," feel free to replace with whatever field name is applicable) with the value from the Inferred Postal Code. The two filters will make sure that you don't write overwrite a postal code if it exists (Filter #1), and make sure that you're not writing a blank value (Filter #2).
Cheers,
Edward Unthank | Founder, Etumos