That’s a good question! I like questions like this that push out the boundaries on some these ideas (a kind of testing to destruction ).
It’s really hard for me to imagine a human child being born not possessing any of the seven higher fetters (desire, aversion and upwards). Though such a person would be at least a non-returner and wouldn’t be reborn as a human anyway, which neatly disposes of that issue.
I can’t recall any examples in the suttas of a sotapanna being reborn as a human (some examples in the deva realms alright). For a sotapanna, their dhamma eye is supposed be open (even from birth I guess). Am not sure that that would be make any practical difference at the infant stage. Though, I guess when they are old enough they should have a deep intuitive grasp of the nature of self/reality/conditionality, quickly grasp which teachings seemed in accord with these intuitions, have a naturally appropriate relationship to rites and rituals, and be likely to find their way to Buddhism eventually, assuming the teachings were available (or maybe they’d be likely to be reborn to a Buddhist family). That’s the theory anyway I guess. Much the same would hold for a once-returner, I’d assume. The fetters of desire and aversion would still be there (just somewhat weaker) so it seems feasible.
For stage of non-return upwards, it’s not an issue (just as well because the model would really break down otherwise).