My child's mother is pregnant and is cutting me out of her life already and telling me she is going to deny me the right to a paternity test and that I will only be able to see our child on her terms

So you laugh and as soon as the child is born you file in court for a paternity test though the court ( she would be in contempt of court if she refuses) You also file for court ordered visits with the child ( again if she refuses, you take her back to court) and you arrange to start paying child support though the court

Also check to see if your state has a putative father registry, and get on it ASAP.

California Courts: Self-Help Center: Free and Low-Cost Legal Help: Get Ready for Court

While I sort of agree with Chuck to laugh at her since she knows nothing about the law, I would recommend refraining until AFTER you file for custody/visitation. If you let her know your plans beforehand she might try bolting.

By the way, you have the same rights as a father, whether you are or were married to the mother or not.