As you’ve mentioned, you did use the F hotkey to create new edges from vertices, however you need to select at least 3 vertices to be able to create a face (polygon). I’m guessing you neglected to do so and rather only filled 1-2 vertices at a time.
Additional info: Blender does produce “pure” edges if two vertices are selected and F is pressed even if this vertices are part of the same polygon. Some other apps do cut the polygon in two. (If you want this then you have to use the knife tool but have to pay attention for correct snapping (the vertices)).