For my orders I always got an order confirmation email, with a subject line similar to this: “Your Purism order receipt from April xx, 2020” and inside the email is info about what you ordered, you order number, how much you paid and so on. I think it should be sent automatically, you should get it directly.
Purism’s support usually answers within a day or two in my experience, seems strange that you got no reply in a week. Maybe try contacting them using a different email address (or calling on the phone?) to rule out that there is some problem with emails not getting delivered to your particular email address?
Edit: for the purpose of testing this and seeing for yourself what the confirmation emails look like, you could try making a 5 USD donation on the https://puri.sm/fund-your-app/ page, that is treated as a “purchase” and gives the same kind of confirmation email as normal orders.
Edit 2: or get a Librem Social account and verify that way that emails from Purism get delivered, as @mirkoboll suggests.