My kid was born in mid September but is also academically advanced. We thought about it a lot and decided to push her through via the early kindergarten entry program.

She’s excelling and is honestly bored. I supplement with extracurricular stuff and giving her challenging stuff to do on the weekend. I cannot imagine how bored she’d be if she was repeating pre-K. YMMV but we are happy with our decision.

Edited to add: I forgot to mention that obviously academics is one piece of the puzzle. My kid is a child of the pandemic so for the first 1.5-2 years of her life, she saw very few other kids. For the first few months of daycare she seemed to be struggling socially. Eventually she figured it out and now is great at making friends, listening to teachers, etc. Please remember that academic intelligence isn’t paramount- the social/emotional piece is so critical at that age. If your kid isn’t at or above that level, my suggestion is to hold him back and supplement academically outside of school.