Users are able to save invoices even if tax periods are not setup under Setup > Accounting > Manage Tax Periods

Check the subsidiary of the Customer or Invoice.

We can save invoices even if the tax period is not setup if the country of the subsidiary of the customer selected is US. US subsidiaries/Nexuses do not use tax periods.

If the subsidiary of the customer is non US, then the system will not allow us to save the invoice, it will give us this message" Insert Transaction Failure: No valid, open, tax period for date - XX/XX/XXX. Please visit Setup > Manage Tax Periods to set up a new tax period. "