@Fr8dog the problem with approach #2 is, sometimes passport is not enough and CoC is requested specifically for background check...
Additionally, just obtaining passport does not fix DB record in USCIS, only in DOS system.
$1400 is a lot, but assuming child is 16 and would hopefully live until at least 80....
80-16 = 64
1400/64 = $22 a year to have ultimate and undeniable proof of citizenship for any life situation