How to shrink big database files faster than dbcc command?
An alternative to the DBCC command in this szenario is what I am
  looking for.


One possible alternative to shrink is described in Paul Randal's article:
Why you should not shrink your data files


  The method I like to recommend is as follows:
  
  
  Create a new filegroup
  Move all affected tables and indexes into the new filegroup using the    CREATE INDEX … WITH (DROP_EXISTING = ON) ON syntax, to move the
  tables and remove fragmentation from them at the same time
  Drop the old filegroup that you were going to shrink anyway (or    shrink it way down if its the primary filegroup)
  


Even if this method will lead to desired result and even more: you'll achieve defragmentation of all your indexes, it is not faster than shrink, it requires additional free space before you can shrink the old files, it can hardly be automated and there will be a problem with LOB data as it will remain in the old FG unless you copy it manually to new FG.