Can you tell me what legal rights I have to my soon to be born child, not in a relationship with the mother, and she doesn't want me to have anything to do with the baby. She's moved house and ignoring my calls. She is originally from Latvia and will proboably move back there in the near future, and I will never see my child, and she will never know who I am.

ANY question on law needs to include your general locale as laws vary by area.

You have the same rights as any father. But you have to go to court to enforce them. Unfortunately you can do very little until the child is born. And without knowing where you are, its hard to advise you o9n what you can do. You should check out this sticky: https://www.askmehelpdesk.com/family-law/putative-father-registry-344695.html

Agreed, hard to say without knowing where this is.

But in US, you will as soon as child is born, file for joint custody or at least visitation rights, You ask court to order that she can not move out of area without court permission

... my soon to be born child, not in a relationship with the mother, ...

The statement that you are not in a relationship with here is incorrect. You were in a relationship with her: you had sex with her. Now, the relationship is that you have a child together.