I regulary checked the appointments on doctolib. Whenever someone cancels their appointment, it becomes available and suddenly you see appointments popping up in the next couple of days. I guess you need a bit of luck. There is also a waiting list that you can sign up for on doctolib, but I found that they do not inform you quickly enough to get the appointment that becomes available. So just keep checking doctolib for the Frankfurt and Berlin appointments (I would focus on Frankfurt). They seem to have more appointments available and they were rellay nice and fast - I was finished in 1 hour and 20 minutes.
You can do the DS-260 as soon as your I-130 is approved and you have a case number. Then you mail all required documents (birth certificate, police reports, I-864, etc.) to the consulate.
Hope that helps!