I wouldn't simply leave him be, as often boredom can turn into resentment. Many adults significantly resent the boredom of their early years of education. I would move him to 1st grade mid-year, even if it costs significant adjustment time.

Time can be saved. His studying can be scaffolded using studying techniques available on the Internet. Spaced repetition, pomodoro method, and other things.

I would prefer to move up. From the research it seems superior to enrichment. Good luck!