Show answer: You cannot.
Long answer: Archiving means that the questionnaire (questions, text, etc.) are stored to an archive file, and the answers along with anything else is deleted from the database.
the webpage asked for a USB key
It should only ask for a key, if you have configured the two-factor-authentification in your account. The login shall ot be related to downloading the data (except, you need to log in to downlaod them). But if the project was archived, then the collected data is deleted.
There is the option to restore the data from the server backups, if the project was archived within 12 months. Yet, this is quite some work to do, so we don't do that for free: https://support.soscisurvey.de/?qa=6/kann-ich-geloschte-daten-aus-der-befragung-wiederherstellen