The moment where Barbara enters the TARDIS in An Unearthly Child was achieved simply by editing, cutting from Barbara pushing against the doors to the scene of her entering the control room. This cut was used as a convenient recording break, enabling the cameras to reposition themselves around the set.
There’s a big difference between the pilot and the remount at this point; if you watch the studio recording of the pilot included on the DVD release, you’ll see that all three takes of the TARDIS interior scene begin with a shot of Barbara pushing open a set of police-box doors. Waris Hussein’s original idea was to have a camera track in to follow Barbara into the control room, an idea dropped on the day of recording. (The floorplan marks that camera position as ‘3C’.)