I’m not sure what you’re asking for. In the first paragraph you say you want a paper pulp, but in the title and second paragraph you say you want chipboard?
It’s definietly possible to mold paper pulp into 3D shapes. Maybe talk to some other manufacturers? There are way too many egg cartons and fast-foot drink trays for them all to be made by one person, so ask around.
As for molding chipboard…I’m not sure. You can bend and laminate plywood but it’s very grain-dependent, so I dunno how well chipboard would work (being full of variously shaped and oriented chunks of wood).