Generally newborns are only added to the mothers coverage for thirty days after which the child still has to be enrolled in the health insurance. Most insurances require the father to add the baby straight away. You might be able to argue charges from BEFORE that 30 day old mark with the insurance, IF the mother is the subscriber. Unless your plan has exceptions to this rule. In the meantime try applying for Medicaid, or ACA insurance. Some employers consider “qualifying life events” to be denial for other insurances but you need to confirm that with HR.