Question for couples that are not married but live together and are having or have a baby.

I read that in the hospital you have to establish paternity if you are unmarried . Me and my so live together and have been together for 6 years and we have a 4 year old already . We live in a different state now from when daughter was born. Since we aren't married will my so be forced to pay child support even though we live together and he is the head of household on our health insurance ?? It also said it takes longer to get a birth certificate in mail for unmarried couples. I'm in Pa just for reference .