It takes a lot of Skin to skin contact from his chest etc to transfer that much cream.
He is molesting the kid
This could just as easily happen if a Grandma was using the same drug for menopause symptoms. The danger of children being exposed to it is clearly stated in the drug literature.
As the medical people contacted believe this was inadvertent, I have to believe the father was just darn stupid with regard to the use of the drug. ,
(If he’d been doing it on purpose, why would he take the baby for medical assessment?)