The first scene was shot. http://www.radiotimes.com/news/2013-09-19/first-ever-doctor-who-scene-filmed-fifty-years-ago-today
Cool moment. However, I feel like the first air date is more important. Otherwise, couldn't we count the first moment of pre-production or the moment the show was approved instead?
Unfortunately, we don't know exactly when Sydney Newman had the idea, but we do know that a few minutes later Nigel Kneale said "No, that's a terrible idea, only a producer could come up with something like that..."
And the first photoshoot http://www.radiotimes.com/news/2013...dio-times-photoshoot-50-years-ago-reveals-all