Can non-Catholic parents ask the priest to baptize the child (infant) in the Catholic church and promise that they will give the child a Catholic upbringing? I mean, it could be a learning experience for the child. Even if the child doesn't believe, such insider exposure may give the child some underlying presuppositions that Western atheists make (i.e. existence of God, the causal relationship between the supernatural and morality, etc.), which may not be accessible to atheists who are not raised in a Christian household. Also, even if Christian morality isn't perfect, the church at least provides a social environment as an attempt to not only teach morality in the Western world, but also promote community service, and Catholic churches are pretty common in the United States, so maybe the non-Catholic/non-Christian parents may willingly take advantage of that. Plus, I use the Catholic church in this question, because I know that the Catholic church seems to consider all people who are baptized are Christian, but not all Christians (in this sense, Catholics) are saved and that salvation is an ongoing process. I think that would be doable for a non-Catholic person who intends to raise his or her child Catholic. Even if the child may not become an observant Catholic in adult life, he or she will forever be Catholic, and the Catholic upbringing may be beneficial.
The Roman Ritual prescribes
Note that "Catholic rearing" must be "guaranteed", and it is the priest who must assess that. He may feel that "infidel parents" may not be able to guarantee it sufficiently, even with a fully-qualified sponsor.
The Ritual recognises that the sponsor (or "godparent") will be an important part of the child's religious upbringing:
... and it lays down rules which need to be met in order that the sponsor is deemed capable of discharging that responsibility:
(In every place in the quotes, lawfully is referring to Canon law. If the parents are opposed and a baptism takes place, there may be a civil case to answer.)