The question ask us to grant write object permission.
You should not give a more broader permission as asked because it's against the principle of least privilege.
objectCreator has this description:
Allows users to create objects. Does not give permission to view, delete, or replace objects.
objectAdmin has this description:
Grants full control over objects, including listing, creating, viewing, and deleting objects.
The objectAdmin has unnecessary permissions that doesn't needed by the question context.
https://cloud.google.com/storage/docs/access-control/iam-roles