|"That's the exit over there, love. I'm having the robot dog back..."|
Colin Baker had to make The Twin Dilemma as his first story due to it forming part of Davison's final season. Sylvester McCoy had to début in Time and the Rani only because of the dearth of scripts available. Christopher Eccleston, on the other hand, filmed scenes for his fourth episode (Aliens of London) on his first day as the Doctor - though Rose did form part of the first recording block. David Tennant filmed his first story first only because it happened to be the Christmas Special recorded prior to work commencing on Series 2.
Matt Smith also made his fourth episode first - with location work on The Time of Angels.
It isn't just Doctors who make their débuts out of sequence. The very first thing Adrienne Hill (Katarina) filmed on Doctor Who was her death scene from her second story. Matthew Waterhouse (Adric) recorded State of Decay before Full Circle. Karen Gillen, with Smith, started with her fourth episode. Bringing things up to date, Jenna Coleman filmed Hide as her first full story.
Of course, there is always the possibility that Capaldi is going to retain the Smith costume - but I doubt it.