Depends on when he stole it, when he picked up Susan (unless she is his biological granddaughter who also escaped with him at the same time), and so on.
"The Edge of Destruction" definitely refers to harrowing adventures prior to "An Unearthly Child" that put in the final missing pieces as to why the Doctor started out so vicious toward Ian and Barbara in the first place, given that they spent a lot of time trying to show him (Susan already figured out they were okay!) that human beings evolved and became more civilized (even if it took thousands of centuries) and even by the time of "The War Games" the Doctor certainly reacts to being told (by the War Chief, another renegade Time Lord) how for half a million years that humans were finding new ways of systematically killing each other, so it's a known fact that humans were rarely seen very kindly by the Time Lords and it's now the Doctor's turn to point out the planet's unique problems and how he tries to help...
He probably did assignments for the Time Lords but, due to whatever catastrophe, ultimately left and either saved Susan, or picked her up elsewhere where she calls him "grandfather" as endearment. There are so many gaps that could be creatively resolved... I prefer the idea he stole what he could get access to (while it was in the shop to be repaired) as opposed to taking the capsule he may have been assigned in pre-catastrophe duties.
