Depends on what you really mean by DSC.
The BDS formulated a scheme on which DSC is certainly based - and based very heavily. I did the BDS Deer Management course with Dieter Dent in 1984 - many of the elements were already quite well developed at that point - the shooting test was near identical to the current one. Chatting with the likes of Richard Prior and Peter Baillie on that course confirmed this. As an aside, those gentlemen were very clear that they saw it as a way of raising the basic standard of stalkers and not least as an organised way to introduce people to the sport. World domination didnt come up in the conversation

An influence was certainly the St Huberts Club scheme.
I'm by no means as certain on the exact development thereafter, but believe BDS took forward and formatted the general question bank as we now know and applied a deer ID assessment that included pelts and antlers in addition to photo's.
The NSCC - National stalkers competency certificate came about and that evolved into the DSC.
Interested parties met at the NSCC stage - including FC, BDS, BASC etc etc and DMQ was formed as a company limited by guarantee and with ownership spread amongst those interested parties. The BDS gifted the examinations to DMQ - and retain copyright if I understand correctly.
And... here we are.
Not claming its a Simon Sharma like definitive history and happy to see others fill in facts/ details.