I’m trying to make a Scene Component be the root of a simple Box StaticMesh, but if I make a Scene Component blueprint, I can’t add any components. If I make a blueprint from the StaticMesh, I can add a Scene Component but not make it the parent.
That’s AFAIK not possible. The SM has to be the root, otherwise it would not be a static mesh blueprint anymore. You could try to reparent it (class settings → parent class).
In the tutorial you reference, the instruction says: “Go ahead and create a new blueprint.” At this point you want to click the “Add New” button in your content browser and select “Blueprint Class.” Then select the “Actor” button. You’ll then have what you need to complete the tutorial.
JTLYK, it sounds like you were creating a Static Mesh blueprint, which would automatically inherit a static mesh as the root component. For this tutorial you just want a plain old Actor blueprint to work with.