So far as we can discover, the expression was originally an American one. The first recorded use is in the
Congressional Globe
for 4 March 1850: “There should be no skulking or dodging ... every man
should ‘face the music’ ”.
It seems then to have had the meaning of
facing hardship or danger. Only in the 1860s did it take on the sense
it now usually has, of taking the consequences of one’s action, or
suffering due punishment for some transgression.
It seems to suddenly burst into popular consciousness in 1850, with
many examples to be found in the years that immediately follow (this
suggests an origin as a catchphrase in popular writing or music, but
none has been traced). One school of thought says that it comes from
musical theatre. A nervous or inexperienced performer would have to
summon up all his courage to face the audience, which would require him
also to face the musicians in the orchestra pit, a cynical and
world-weary group who had seen everything.
A second theory is that it is of military origin, though no two writers
agree on what that might be. Explanations include a soldier taking his
place in the ranks during an assembly, so facing the military band; a
cavalry man trying to keep his restless horse quiet while the band is
playing; or a soldier being drummed out of his regiment.
You should always try google first!