Max,
Unfortunately, I can only offer some general and obvious hints:
- Baddeckenstedt (with an "e") is a small city 10 miles from the city of Hildesheim. Till around 1800 it belonged to the "Hochstift Hildesheim" (a political entity).
- Burgdorf is a small village close to Baddeckenstedt, the family may have been named after it originally
- Have you tried to search through the church books of Baddeckenstedt to see if Julius' birth is recorded there?
- Same for his marriage, this would probably give his birth place and parents. Is it in the Baddeckenstedt church books?
-Potentially the city may have kept records of people living there ("Meldekarten") although that may have only started a bit later - have you contacted the city of Baddeckenstedt for that?
- Do you know more about the wife's origin in Berlin, e.g. where she was baptized? The couple may have married there as well.
Good luck with your search,
Nils