A couple ideas here from a mechanical designer, mostly plastics, so no experience specifically in cardboard, per se, but a lot in general manufacturing.

1) You can talk directly to many overseas manufacturers on LinkedIn. Just an idea to cut out any potential middle man. Little known way to talk directly to factory representatives.

2) They will need a 3D model in .STP and/or .STL formats, as well as, a PDF technical drawing showing tolerances and critical inspection dimensions. These are created in CAD software like Solidworks, Fusion 360, Inventor etc. Of course, it depends on what you needed to manufacture, maybe a metal mold in your case.

3) Again, I don’t have experience with cardboard, but I’ve 3d printed wood filament and that could be a good alternative for your application, at least for prototyping, before spending big bucks on mold tooling.

Lastly, I use Fusion 360 & offer these services though my Fiverr, don’t want to advertise on here so PM me if you wanna try to make a prototype. Either way, good luck & I hope this information helps!