As is well-known, the format for Doctor Who was to alternate stories set in human history, and science fiction stories. (Script editor David Whitaker originally conceived of a third category, 'sideways' stories, but there are few examples of that, with only 'The Edge of Destruction' and 'Planet of Giants' being plausible candidates, and it's clear that this category soon got subsumed into the more general sf stories.) These two strands are represented by the audience's viewpoint characters, the science teacher Ian Chesterton (William Russell), and the history teacher Barbara Wright (Jacqueline Hill). Both take an interest in Susan Foreman because she is a prodigy in both subjects. (In Whitaker's novelisation Doctor Who and the Daleks, he adds some nuance here, making Susan very good at some historical periods, but dreadfully ignorant of other events, such as the Spanish Armada.) This is reinforced by Susan reading a book on the French Revolution, in which she spots an error (a scene, incidentally, not in the original pilot). In retrospect, we are meant to realise that she identifies this error through her personal experience.
When we finally enter the TARDIS control room in the first episode, it is a mixture of the advanced and the antique. The control console, and the walls, are a science fictional mise-en-scène, but scattered around the control room are various antique objects: a clock, a tripod of birds (Whitaker talks of a bust of Napoleon). The number of these objects in the TARDIS declined as the years went on.
In the next episode, 'The Cave of Skulls', Susan talks about the TARDIS appearing as an Ionic column or a sedan chair, both antique objects.
More importantly, the remaining three episodes of the story include the first shown trip into Earth's past, to the Stone Age. In The Television Companion, David J. Howe and Stephen James Walker say that it is not necessarily the Stone Age of Earth depicted, as this is never established on screen; but if a planet is presented that looks like Stone Age Earth, it is probably safe to assume that it is Stone Age Earth, until someone says otherwise. That this story is a historical is suggested by its being immediately followed by an sf story, 'The Daleks', and the alternative title of '100,000 BC' also suggests that someone thought the story was set on Earth (though it's not clear when it acquired this alternative title). Indeed, no-one else involved in the production of the show has ever suggested that it isn't Earth, so the idea that it isn't can be discarded.
That said, it's a risky strategy for the first historical to be actually a prehistorical. There's a sense that what we are getting is more common assumptions about Stone Age humans (living in caves, dress in skins) rather than anything based on actual research into the Middle Paleolithic (as professional paleontologists recognised at the time). And everyone is portrayed by RADA-educated actors talking about themselves in the third person because that sounds 'primitive'.