Your end of month processing can begin as soon as you like, and sometimes in advance of the end of the month if you are sure there will be no more activity.

e.g. if you decide to stop invoicing customers 2 days prior to the end of the month, then you can run and issue statements in advance.

Some end of month activities are entirely in your control (e.g. entering new sales invoices) while others are outside your control (e.g. supplier invoices received in the mail after end of month). You should make your own decisions on what a reasonable cut-off date is for some of these things.