Gee Wizz - that's it, why didn't we think of that? - WOW! So, for you the fact that no application for US citizenship has been disclosed is proof enough that it doesn't exist! Amazing - that's a real brilliant piece of sleuthing. So with that premise so unequivocally established there's no point in assuming that any other records exist either, is there?
Medical Records
Occidental College Records
Columbia University Records
Harvard University Records
Birth Records
University of Chicago Records
Pssssst.....Hint: There probably wasn't any application for US citizenship ever filed, and for a minor that would have had to be done by the mother. I know you are very well educated and smart 'cuz you tell us peons all the time, but Alas! you may want to consider that lack of an application form on file does not mean a lack for it's necessity or existence. ....Just a thought.......