Defining “citizen at birth” doesn’t help to define “natural born citizen”.
The only gap to be found is in our knowledge, not in the Constitution. The term had a definition in 1787, and the framers understood it. (Otherwise we’ve got them writing nonsense.)
We’d be better off hunting down their definition than trying to shoehorn ours into the document they wrote and ratified.
“citizen at birth” is equivalent to natural born.
You can probably “hunt down their definition” by actually doing some research on this subject - as I did! :)