An open invoice is only displayed to the customer 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 subscription (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».
So check your payment settings and whether the customer invoice is already due. As soon as it is due, it will be automatically displayed to the customer. Otherwise, you have the possibility to change the invoice date manually. See also: Invoices and finances explained
If it is desired that an invoice is due immediately, it is recommended to use the default setting «Date of invoice = Purchase date».