The first ever doctor who episode has been lost. it was destroyed by the bbc in the 70s while they were cleaning up their warehouse. Only clips exist from the first ever episode. And most of the original series featuring the first 3 doctors has been lost forever. Only a few remain. :'(
No, the very first episode was An Unearthly Child, it's even on youtube. There are missing episodes but this occurred from 1964-1973 (the first episode was in 1963)
I just looked up, the original pilot episode was lost but then rediscovered in 1978 in a mislabeled film canister it survived purely by chance. And before then it was thought lost forever. Check it out on the original doctor who imdb trivia page.
But oh my god I fucking want this
(And I am now satisfied, thanks for telling me where this was. :S)