You do not need to be in possession of the HFC in order to buy tickets with HFC reduction. In theory you could even wait till you are here before getting the HFC. When buying tickets just select the HFC reduction.
It is on the train that you will have to show the HFC and the ticket. The HFC is needed to travel with half price tickets, it is not needed to buy such tickets.
If you have landed on the page where SBB checks your identity you are probably trying to sign up for the little red card that is confusingly called “Swiss Pass”. That is a card that had your photo on it, and that is used to store commuter passes etc… It is aimed at residents.
To buy the 1 month HFC you only need to create an account, you do not need to go through the identity verification. That will be done on the train.