first of all: Your problem is a well-known problem for German people too, it's really hard to find a kindergarten place in major cities. Many parents apply for a place even in a kid's pre-birth time these days to improve their chances.
Do you kow the service of "Elternbüro im Kalk Karree"?
Hopefulley the can help, see details here: http://bit.ly/2aLnWFs
All the best!