first bath of the year
Refers to the first bath taken in the new year, often at a public bath or hot spring, sometimes with special herbs or rituals.
baby's first bath
Used for a newborn's first bath, a milestone event in early childcare.
It is said that taking the first bath of the year on New Year's Day will keep you healthy all year.
The midwife helped with the baby's first bath at the maternity hospital.
Compound of 初 (hatsu, 'first') and 湯 (yu, 'hot water; bath'). The exact historical origin is uncertain, but the word follows a common pattern for 'first X of the year' expressions.