I'm just wondering as to how I would achieve this, as I could not find any documentation on it inline.

The effect is as follows:
There is an open container of sorts (for example, an open box). When the camera looks into the opening of the box, or even enters it, it is seen that the space inside the box is bigger than the space set by the bounds of the box, potentially even infinitely large.

The popular example is the TARDIS from Dr Who

No sneaky camera angles and then cutting away with this one, the camera needs to smoothly move inside the container.