Lot's of luck. If you knew what town in Mecklenburg-Schwerin, you would easily be able to find her birth in the parish records for that town. The Mecklenburg-Schwerin census is probably not going to help because the 1819 census was before her birth. The 1867 census might help but Sophie or Sophia is a very common name for a girl in Mecklenburg-Schwerin and unfortunately, the census for 1867 only gives the year of birth. So, it is not very likely that you will be able to find Sophia in the 1867 census. But try searching for Sophia Baade's and see how many there are. If you knew a town in M-S, it would be a straightforward exercise to find her birth record(with microfilms borrowed from LDS).

The only other option I can think of is the year of immigration. People who emigrated from Mecklenburg-Schwerin were supposed to apply for permission from the authorities. You can write to the archives in Schwerin and see if they have such an application on file. This an expensive application search (~$100) and there are not applications for everyone. All of my maternal great grand parents came from Mecklenburg around 1870-1890. There was an application from only one of my great grand parents; whether the others ignored the requirement or the applications were lost, I haven't a clue.