Can you give antioxidants to a baby to prevent hie?

No. The only way you can prevent hie is to make sure that every thing goes well during the pregnancy, during the delivery etc. Having a well trained health care professional in the delivery room is a kind of insurance and reassurance but cannot be total hie proof. Vast majority of hies are not preventable. Their severity can be decreased with the help of head cooling (cool cap) or total body cooling.
No. In theory, antioxidants may have a role to play during the recovery phase of hypoxic-ischemic encephalopathy, but this has not been well-studied in humans.