How to move all files whose contents begin with 0?

There isn’t a command to do this. However, it’s a straightforward piece of scripting.

1. Work out how to identify a file by its contents and move it:

   f=example_file.txt
   b=$(head -c1 <"$f")
   [ "$b" = "0" ] && echo mv -- "$f" zero/
   

2. Work out how to iterate across all the 100,000 files in the directory:

   find . -maxdepth 1 -type f -print
   

   Or maybe your shell allows you to use a wildcard for a large number of entries and the simpler more obvious loop will work:

   for f in *
   do
       echo "./$f"
   done
   

3. Work out how to run the mv code for each possible file:

   find -maxdepth 1 -type f -exec sh -c '
       b=$(head -c1 "$1")
       [ "$b" = "0" ] && echo mv -- "$1" zero/
   ' _ {} ;
   

   Or

   for f in *
   do
       [ "$(head -c1 "$f")" = "0" ] && echo mv -- "$f" zero/
   done
   

4. Optimise the find version:

   find -maxdepth 1 -type f -exec sh -c '
       for f in "$@"
       do
           [ "$(head -c1 "$f")" = "0" ] && echo mv -- "$f" zero/
       done
   ' _ {} +
   

In all cases remove echo to change the command from telling you what it would do, to doing it.