I know that one can convert an infant (and if he doesn't recant when he becomes of age, the conversion is retractively chal) but what about milah? For a Jewish child, milah before the 8th day isn't a valid milah and hatafat dam brit would have to be done at the proper time. But a non-jewish child isn't commanded to get a milah so it would seem that there is no obligation to do so on the 8th day specifically. (By the way, this is not a duplicate of the comments in Why Not Eight Days Until a Convert's Circumcision?) This site http://www.convert.org/Converting_Infants.html reads, regarding converting a newborn, "If possible, this should be done on the 8th day after the birth of the boy. If a circumcision has already been performed, a drop of blood needs to be drawn in a ceremony called hatafat dam brit." but no source is given. Why would there be a requirement to wait till the eighth day? A Jewish baby lives through one shabbat (i.e. 7 day cycle) before a brit but the non-Jewish baby has no connection to shabbat.
Is it that, objectively, there is something halachicaly about being alive 8 days for any human that then makes milah viable (I don't mean medically and I'm not sure if the kabbalistic notion of "positive and negative energies" http://www.nymohel.com/laws_customs.php#p16 is an answer I, as a layman, can truly appreciate).