Can I get visitation or custody/time sharing, even though I am not on the birth certificate?

If you are not married to the mother of your child, and you are not listed as the father on the birth certificate, you can still seek custody and time-sharing of that child. What you would need to do is to look for an experienced family law attorney that could assist you in filing a paternity action. By filing the paternity action, you can ask the court to establish a parenting plan and time-sharing schedule so you could exercise time with that child.