What you want is indeed possible and is called quick search mode. Quoting from the man page:
The Quick search mode allows you to perform fast file search in file panel. Press C-s or Alt-s to start a filename search in the directory listing.
When the search is active, the user input will be added to the search string instead of the command line. [...] When typing, the selection bar will move to the next file starting with the typed letters.
You should also note that this is the default mode when the command prompt is disabled (this is controlled by the variable command_prompt
in the ini file, default location ~/.config/mc/ini
).