My understanding of this situation is that the ticket you purchased must be displayed in a position that is “reasonably” viewable by the “officer” issuing the parking ticket given the prevailing circumstances. The fact that you may be able to prove you purchased one before the offence was recorded is irrelevant.
There have been many cases where (for instance) the driver left his window slightly open and the parking permit had blown on to the car floor but the offence is not displaying the purchased parking permit not failing to purchase it in the first place.
Unless you can prove that the permit you purchased was not displayed because of “an act of god” or find an irregularity in either the process of issuing the summons or any contained paperwork then your case will fail.
I would state in writing that you did purchase a ticket but after you parked the car and forgot to display it, they might take a lenient view.