Not everyone who left Baden applied for permission to emigrate, but others of the same surname may have emigrated at another time. When tracking an ancestor with an uncommon surname who can't be identified in the database, it may be worthwhile to search the church records of the towns where others with the same surname originated.
Since Germans often were known by a middle name (some were given three middle names), it's a good idea to review the record of each person listed under an ancestor's surname. Someone known as George Bower in the United States may be appear in German records as Georg Bauer or Baur. Michael Palmer could be listed as Georg Michael Balmer.
Copies of the original emigration records may be obtained from the Family History Library in Salt Lake City.