The Picardy third was likely “invented” during the baroque period by the likes of composers like Bach when equal temperament came into being. Listen to the Bach Preludes and fugues and you will hear them quite a bit.
Sometime in the Renaissance - there are plenty of 16th century examples.
My personal suspicion is that the use of the Picardy third developed along with the shift in keyboard instruments from split-key Pythagorean tuning to quarter-comma meantone with twelve keys per octave. In meantone temperament minor thirds are flat compared to Pythagorean tuning, but the major thirds are pure (or at least the majority of them are).