The title pretty much says it all. The simple First Person Blueprint template has this problem. It looks good in the editor, but as soon as you launch the game, the camera and all its children fall to the center of the capsule.
For camera offset within the character blueprint, use a Spring Arm component and link the camera to it. Then you can set a spring arm length and all sorts of cool stuff like collision detection for avoiding camera clipping and lag for giving a more cinematic smooth movement to the camera.
A spring arm of a first person camera?
It didn’t sound like you wanted to use a first person camera 
Did you mean Vertical offset?
Offset from all axis get ignored but the most problematic is obviously the vertical one indeed.
So thanks to Opamp77 on the forums, I’ve found a solution:
You basically need to add a scene component on which you set your offset, and then put your camera and any other children under it.
Well that’s screwed up. Good work. You should answer your own question to help people in the future.
Done! Thanks!