How long does it take to process an application for basic health insurance?

Hello, I hope to get a lot of answers here. Have you ever applied for a basic plan with a private health insurance provider in Germany , regardless of which one, and how long did it take until you received approval and were then insured?

I need to provide proof of insurance for university, and I'll need it soon. Please only reply if you really applied for the basic plan . For example, with Allianz or another private health insurance provider.

Thank you in advance.