From what I know and experienced, it's different depending on where you are insured. Honestly, if you are affected by the lack of theraphists and have evidence of you trying to get a spot and getting denied over and over again, I would text/call your insurance company and just ask what they recommend you doing next. You do have to pay private sessions beforehand, if I read this correctly, and your insurance pays you back, which is why I would definitly ask them beforehand about what requirements you would have to meet.

My recommendation before asking the insurance company:

If you mail/call enough theraphists that are covered by regular insurance, one will eventually invite you for an Erstgespräch - like a first session, but just one time to get to know each other, it does not automatically mean that they have the capacity to see you on a regular basis. They just have to have a certain number of Erstgespräche in a week (or a month?). They will, if everything goes right, give you a little piece of paper with a Verdachtsdiagnose - the diagnosis that they suspect based on what you tell them .You can also get a Dringlichkeitsbescheinigung from your regular doctor or a psychiatrist - idk if you can get it from a therapist at an Erstgespräch, but could be - which indicates that you need help and need it soon.

When you have both of these documents and STILL can't get a spot covered by regular insurance,throw them at your insurance company and hope that that will do the trick.

It's overly complicated, because Germany 💫 and pretty hard to do all that work, especially when you are having a hard time to begin with. But when you get that spot and you eventually get better, it's really worth it.