Fresh install on used macbook air

Hello I recently purchased a used macbook air 2012 that had some damage, I fixed the main issue but the airport card is trashed and I have removed it entirely until a replacement arrives. Currently I'm using a usb-wifi dongle to connect to the internet which works great except I cannot sign into imessage or the app store because it says it can't verify my appleid.

I'm guessing this has something to do with the previous owner whose name still appears in the Home finder folder. I would like to do a fresh install of OS without her appleid or anything so that the machine is fully in my control. The problem with this is that I cannot use internet recovery since I have no airport card, I can only connect to wifi once in the OS and the 3rd party software auto-connects to my wifi. Also I can't download the OS to a usb storage stick since I can't verify my appleid in the appstore.

What are my options here to do a fresh install without internet recovery and without being able to access the appstore?