There isn't a way that I know of to make default fields accessible to the global search but you can make custom fields accessible.
You should be able to make a custom field that stores the value of the Inventory Number. Custom fields have a checkbox of "Global Search". The field must store the value so you will need to make sure that it updates if the Inventory Number ever updates (workflow/suitescript).
From NetSuite article 8403 titled "Including Custom Fields in Global Search":
To index a custom field to be included in global search, a user with
permission to edit or create custom fields must check the Global
Search box on the custom field record. By default, the Available for
Global Search box is not checked for preexisting or new custom fields.
Global search indexing is available for the following data types, when
the Store Value preference is enabled:
Currency
Decimal Number
Email Address
Free-Form Text
Help
Hyperlink
Inline HTML
Integer Number
Percent
Phone Number
Text Area
You cannot index a custom field for global search if None is
selected for any Level for Search/Reporting option on the Access
subtab of the custom field record.