The phrase "first bath" refers to the very first time someone or something takes a bath or gets cleaned up, usually after being born or dirty for a while. Full definition
Fast forward a few weeks to my son's first bath in the baby bathtub. (babybunching.com)
Another example is that some hospitals wash baby upon admission to the «nursery,» while others delay baby's first bath for 24 hours after birth. (tranquilomat.com)