Joe Bauher lists only 10 preproduction prototypes were made in May of 1944. These were tested for quite a long time, and for whatever reasons (delays, new tooling, whatever) production lines didn't pump out models until December.
Now, I've seen combat reports of 64th Sentai with Ki-43-IIIs engaging spitfires and such in Jan 1945 and Feb 1945, but I haven't seen anything earlier than this. The majority of the few-hundred Ki-43-IIIs built saw limited homeland defense in 1945. Burma is one exception, although the Ki-43-IIIs there were definitely not as much of a game-changer as WMaker would suggest.