Is it possible to break the sound barrier with a punch?

I dont beleiev so. Both Mohammad Ali and Frank Dux (Kumite) were very fast but evidently they did not break the sound barrier. If they had done so it would surely have been reported. Not only this but one would hear the sound of the barrier being broken and this would be unmistakable to everyone present and would heve been recorded in the movies of these personalities.
The fastest punch recorded for Dux was 0.12 seconds (fastest punch with knockout). His fastest kick was recorded at 73 mph... nowhere near the sound barirer.
The movie "Bloodsport" - 1988) was based upon his world championship match from which he retired undefeated.

Not with a punch.

If you want to break the sound barrier with muscle power, use a whip. The crack of a whip is actually a small sonic boom, created when the tip of the whip breaks the sound barrier.

Break the sound barrier? no
Break your whole arm? yes

not physically but with a whip or a slingshot effect

Nowhere near.

Technically, probably. In reality, probably not.