An open invoice is only displayed to the member when it is due. By default, this is the case from the date of purchase. You have the option to set your invoices so that they are not due until the first day of the pass (start of the validity period). This can be set in the admin area under «Set up my studio» - «Further settings» - «Payment settings» - «Date of invoice». If it is desired that an invoice is due immediately, it is recommended to use the default setting «Date of invoice = Purchase date».
So check your payment settings and whether the member's invoice is already due. As soon as it is due, it will be automatically displayed to the member. Otherwise, you have the possibility to change the invoice date manually. See also: Invoices and finances explained