A Kitagutschein is valid for 6 months. You can apply for kita spots without having a valid gutshein; and since queues can be 2 years long it’s quite common to do so. When you apply for a gutschein it can be as fast as one week for you to receive it.
Some Jugendamts assist parents in finding a spot. However, because of the current situation most of them stopped this service.
There are Kita Consultants who basically will do the above process for you for a fee. We don’t list kita consultants because we can’t verify their services. You may find them in relevant facebook groups offering their services.
We feel your pain - don’t panic. You’re in the same boat as thousands of other parents. The best we can do is recommend you either hire someone to do this for you; or you grind it out using the process above.