When we first met the Time Lord known as The Doctor, he was already about 900 years old. (Which proves River Song's point: "The Doctor lies.") Think of all the adventures he had in those earlier centuries of his life. We'll probably never get to experience those adventures (at least in the Toobworld Dynamic) unless they recast the role of the First Incarnation with a younger actor.
One adventure they would have to address would be about the Doctor's grand-daughter Susan - was she the child of Jenny from the episode "The Doctor's Daughter"?
Inner Toob had a suggestion for an actor to eventually play the role of the Doctor, James Buckley. But I'm thinking now that he could also play the First Incarnation at an age before the Time Lord became such a stodgy old man.
At any rate, in the meantime, we do have a way to see what the Doctor of those early adventures might have looked like. And that's thanks to pictures of William Hartnell as a younger man, either in screen captures or publicity photos.
For today's marathon we have one of these pictures - thanks to the High Council of Time Lords. This is a publicity photo from when William Hartnell was about 25 years old.