All you need to enter is your NIE and date of birth.

In my own case, it said new licence posted to me 24th July but it only arrived in Correos Camposol on 5th August.

Here’s the Tracker link:

https://sedeapl.dgt.gob.es/WEB_EST_PERSEO/

Note: In their faqs it states:

The application tells me that the permit was sent to the Post Office more than two weeks ago but it has not yet arrived, what should I do?

The temporary permit has three months, even so, after a reasonable time, we advise you to claim it.
To do this, get in touch with who will carry out the procedure related to your license: If it was a renewal, talk to the medical centre where you carried out the examination and in the case of issuance of new permits, it will be with your driving school with whom you must talk to solve the problem. In the case of duplicates, you will have to communicate the incident to us.