Language school Visa (Berlin)

Hi! So I enrolled for a German course at Protected content starting October 7th! I spent some time here during the summer and decided to move thinking I'd be able to apply for a student visa upon arrival (limited information online until I found the Auslanderbehorde site here) but it looks like I can't get an appointment until January. My EU tourist visa expires in 30 days and I'm looking to see if anyone has tips on how I can get an appointment sooner? Whether it be showing up without an appointment...? I can't imagine flying all the way home and waiting until January to come back. Any help?! Thank you!