Dico rubber plate machine

My understanding of the process is that first you make a mold from the assembled type form, then pour a prepared mixture of the rubber into the mold and cure, or vulcanize, it in the machine with heat and pressure to make a flat back parallel to the face of the stamp, then that rubber plate was mounted on a prepared handle, or could be used in a machine to print on materials that would be difficult to print on with metal type. Since rubber stamps are still being made the raw materials ought to be around somewhere.

Jackson Marking Products sells vulcanized rubber stamp materials at their site https://rubberstampmaterials.com/
Go to the Rubber molding supplies section, and the Vulcanizer accessories section. The raw supplies, sheet rubber and matrix board have a limited shelf life.
They can also make dies and molds for you, see the Diemaking services section.
I had some literature that explained the process, now lost, and there has been some web information, but you really have to dig.
In theory the hardest grades of photopolymer can be used as master dies, but for me they just delaminated. Molds made from slug forms were easier.