Gallifrey and the Time Lords certainly didn't appear for a good long while (not at all in any of William Hartnell's series). The impression given in Unearthly Child is that The Doctor is a loner like HG Wells Time Traveller, and built the TARDIS himself. Susan certainly says she made the name up from "Time And Relative Dimension In Space" - although later it was treated as the Gallifreyan word for a Time Lord's conveyance.

I think originally they had a vague idea that he was from the future when the Earth had evolved new races (like HG Wells Eloi and Morlocks), and had been exiled from there somehow.