To date there is no indication that it survived. As it was the only episode of Doctor Who never transferred to 16mm or 35mm film recording, it was never sold outside of the UK and it was produced as a throwaway (which is why it does not connect to any other episodes within "The Daleks' Master Plan"), meaning it was never intended to be kept. So any of the usual sources for finding lost episodes (foreign broadcasters, film collectors) do not apply. The only hope is for a viewer to have pointed a film camera at the screen during its one and only broadcast on Christmas Day 1965 and for that film to have survived (it was due to a viewer recording the audio that allows us to at least know what it sounded like). One can never say never, but of all lost episodes, this (and possibly "Mission to the Unknown" which was also never sold outside the UK but was transferred to film at one point) are considered the episodes least likely to ever be recovered.