I’d guess two of those hoops would be:
[ul][li]proving that the child was not kidnapped and abandoned[/li][li]showing the court that, out of all the candidates wishing to adopt this particular child, the court granting his request, instead of another candidate’s, to adopt is in the best interests of the child[/ul][/li] Mexico Adoption has this to say:
and
So, presumably, the courts will expect officials to conduct a search to find any surviving family members of the foundling. And, reading those two bits from that site, it looks as though the court will grant first a provisional or temporary adoption decrer, then after six months a final adoption decree will be granted.
That site has more information, including requirements for the child to be eligible for adoption.