Yes. For 30 days at least. Newborns are covered by your heath insurance for the first 30 days without needing to do anything. Your health insurance policy will detail the coverage, but your baby is covered. After 30 days, if nothing is done, then the baby loses coverage.
During the first 30 days, you should contact your health provider and add your child to the coverage. If you are under a group plan through your employer, this is called a “qualified change in family status” and is an easy change. If you are on an individual plan, call your agent.
If you have missed the 30 day window to add your baby, then you may have to wait until the next enrollment period. If that happens, you would most likely want to get individual health care coverage for your baby for just the gap period.