Can a wood cabin be laid directly on a existing concrete foundation if a DPC is added?
A damp proof course (DPC) is required “Under Floor Space” where there is evidence that the “water table rises to within 6” of the building perimeter or if surface water does not readily drain away from the building”. (See ICC 1807)
Likewise, wood joists within 18” of the ground or beams and girders within 12” at the perimeter or under a building in a crawl space shall be “naturally durable or preservative treated wood”. (See ICC 2304.11.2.1) Btw, this will help anchor the building to the foundation in seismic and high wind areas.
Likewise, under floor space shall have ventilation through the exterior walls, except where it’s a basement or cellar. (See ICC  1203.3)
Likewise, under floor insulation is required of R-25. (See ICC Table N1104.1(1)) Vapor barriers are installed on the heated side where the building is heated predominantly throughout the year.
So, to answer your question, yes you can install your cabin as you describe with the above requirements, including crawl space vents.
Your situation is a little different because you really don’t have adequate space for crawl space vents. In this case, I’d recommend you eliminate the floor insulation and increase another element in the building envelope. (See ICC Section N1103 Alternative Systems, i.e.: thicker wall insulation, thicker ceiling insulation, better insulated windows, etc.)