There is a surprising number of Americans in this situation, though less than their used to be, partly by virtue of the fact that having an ID is not required and unnecessary as a practical matter for much of the 20th century. You'd have Americans with no birth records (used to be pretty common) who grew up overseas when a passport was not required, such that they didn't even have incidental records of their existence. It also used to be somewhat common in very rural areas. Consequently, there used to be a significant number of Americans who basically have no discernible record of existence prior to their teenage or early adult years. My mother is an example in fact.

It used to be, as of a few decades ago at least, that you were whoever you said you were and the ID offices would happily accept informal artifacts (like family Bibles) as corroborating evidence, particularly in regions where record-less Americans were endemic. Once you got your first ID, you could chain off of that. These days I think it would be viewed with much more suspicion if a person was record-less.