My child’s father refused to be at my child’s birth and isn’t listed on my child’s birth certificate. Can I get a divorce workout him being involved?

You can't sue your husband for divorce without involving him, because you need to serve him with the papers, file proof of service with the court, and give him an opportunity to answer the complaint. If he chooses to ignore the papers, you can get a divorce by default. Since you were married when you conceived your child, your husband is presumed to be her father, whether or not he signed the birth certificate or chooses to acknowledge this fact.  If you sue him for child support and he challenges paternity, he and your daughter will be required to submit to blood tests.  Unless he successfully challenges paternity, as the non-custodial parent, your husband will be required to pay child support, and you can get an order of support in the course of your divorce. And you should. Regardless of whether her father wants to be in your child's life, he still has an obligation to provide financial support for her.  And paying such support can create an incentive for the father to take steps to create a relationship with his daughter. Which you should encourage. A child should have both parents in their life unless there is a very good reason not to.