PCB Pressure copper connectors design
Well... IMHO this will not work. For tree reasons - first, you connector seems to be 3d-printed. It is very hard to achieve absolutely flush and secure mount of those metal contacts in such a primitive setup.
Second - even if you somehow mount the contacts flush, you still have to make sure the whole plastic frame is flush with PCB. It does not sound like you have some kind of spring-loaded mechanism for that.
Third - the surface of those metal contacts looks very uneven on the photo.

Combine all three and you'll see that chances of getting reliable connection every time are very slim.

The best you could do is mount a pair of pogo pins per contact on PCB and make sure your "cube" is pressed down hard and also restricted from sideways movement (e.g. by making 3d printed square "socket" with holes for pogo pins that you would mount on PCB).

Also, check out thousands of readily available spring loaded connectors. You may just find something suitable and definitely better quality than you can make yourself. They are often used in mobile devices as battery/antenna/charging coil connectors.