UPDATE: I should have mentioned, Mozart was born in January, 1756.
Now if you are thinking that these were some sort of stunt with the music actually being written by his father, an established composer and violinist, not at all. Even years before this, Mozart was already correcting his father, rather than the other way around. Yes, by age eleven probably and certainly by age twelve, Mozart was a fully accomplished opera composer who had already written operas in three different languages. These are not "student" works of dubious accomplishment, but quite acceptable operas. Certainly they are not at the level Mozart would achieve later in life, no Don Giovanni or Magic Flute, but perfectly decent operas.
The opening theme of the overture to Bastien und Bastienne is very similar to the opening theme of the Eroica Symphony by Beethoven:
And here is La finta semplice, the whole opera, but with the recitatives omitted. Barbara Hendricks (Rosina), soprano; Siegfried Lorenz (Don Cassandro), bass; Douglas Johnson (Don Polidoro), tenor; Ann Murray (Giacinta), soprano; Eva Lind (Ninetta), soprano; Hans Peter Blochwitz (Fracasso), tenor; Andreas Schmidt (Simone), bass; Kammerorchester "CPE Bach", conducted by Peter Schreier.
The list of composers who were accomplished enough to write full-length operas at age eleven or twelve is a very short one indeed. There is only one name on that list: