One thing you can try, add the Due Date field to the Invoice Template.  The default due date is the day the Invoice is created.  If you add this field you can set it another day in the future that you would like and then the invoice will not be considered past due.

From the Invoice click the template menu at the top and choose to either create a new template or Edit the existing one

Layout Designer will open allowing access to modify the template

Go to the Invoice Fields section and the Fields tab

Put a checkmark next to the Due Date for the Screen Section 

Save the changes to the template (or save it as a new one)

Back on the Invoice with the modified/new template selected you should see a Due Date field on the invoice

All you need to do now is set the Due Date to a day in the future and the Invoice will no longer be Past Due as soon as you create it.

Terms will do the same thing, they are linked to the Due Date.  So depending on what Term you select this will update the Due Date field correspondingly.  With the Due Date field on the Invoice form, if you set the Term you will see when the Due Date is pre set to.