My process was a bit different from the course for this. After adjusting the size and position, it made sense to me that if vertices are deleted, what remains should connect together. Well, that wasn’t exactly true in the end, but it seems I had the right idea about it. I played around with all the options that pop up after you try to delete vertices, faces and edges and “Dissolve edges” is apparently what I was looking for. This also helped prevent any unnecessary geometry from below.
Edit: I see deleting and dissolving was covered in the next lesson. I should clarify that the way I used it was to just dissolve a single edge from the cube and that made things immediately connect, rather than manually attaching more faces to things I deleted