This is a Frame Challenge
Other than understanding a little bit more about the physiology of the child, you won't learn that much.
In your scenario, you only have two ways to raise the child (we'll leave ethics out of this for a moment).
- Raise the child as a feral child.
In this case, the child is raised with no human contact. If... (and that's one whomping big IF), if you can successfully raise the child in a way that the only behavior you see is the "natural" genetic behavior of the "animal" (as in "human animal" if we're talking about feral human children), then you can learn a little bit about the basic motivations and primal behaviors of the species.
The reason this is a huge, huge IF is what, for lack of a better term, we'll call the "Heisenberg alien uncertainty principle." Boiled down, you can't measure something without affecting that something. You can't raise the child with robots without that affecting it's behavior. You can't raise it with (proverbially) wolves without that affecting its behavior. You can't raise the child without affecting its behavior unless, at best, you mimic its original "natural" habitat... which you said you can't do.
Consequently, this path has next to no real value other than to show you the bodily machine in operation, which would help a bit, especially if you want to do things like experiment with
biological warfare pharmaceuticals.
- Raise the child with human help
Frankly, from the perspective of trying to better understand the species, this is even worse because the little angel is going to reflect the human behavioral and emotional patterns. The aliens came to us, right? That means they are intelligent, capable of learning... and therefore the cute little munchkin will quickly absorb every human pattern it's exposed to. That will effectively mask each and every behavior you're trying to research with the theoretical condition of extreme psychological conditions, which wouldn't exist (IMO) in a successful space-faring civilization anyway as such would tend to be antisocial and have been bred out of the species just as it has in ours.1
Is there an alternative?
No, which means that you'll be working with both paths to synthesize the best understanding you can. Your scientists know that a big pile of knowledge will actually be a big pile of rotting Kim-Che, but their superiors won't know the difference, and if they write long enough treatises on the subject, nobody will take the time to read them to discover the conclusions were pulled out of thin air anyway.
But why can't the effort be more valuable?
Because of that "Heisenberg alien uncertainty principle." Because you cannot (and do not) know anything at all about the environment the alien child would normally be raised in, anything you try can and will taint the outcome. You will never see the "true" behavior of the child. Worse, you will never know if what you are seeing is "better" than what you would have seen had you run the test another way. You will always be uncertain. Consequently, you will never have an outcome that will realistically improve your capacity to understand the psychology of the aliens.2
But that wasn't what I actually asked...
True! What you asked was how to ethically raise a child you know nothing about. The problem is, whose ethics?
Ethics: moral principles that govern a person's behavior or the conducting of an activity. (Google definitions)
Ethics are defined by a society. They are not intrinsic to a species. They're a lie — an important lie. An incredibly important lie, but a lie nonetheless.
HUMANS NEED FANTASY TO BE HUMAN, TO BE THE PLACE WHERE THE FALLING ANGEL MEETS THE RISING APE.
“Tooth Fairies? Hogfathers? Little—”
YES. AS PRACTICE. YOU HAVE TO START OUT LEARNING TO BELIEVE THE LITTLE LIES.
“So we can believe the big ones?”
YES. JUSTICE. MERCY. DUTY. THAT SORT OF THING.
“They’re not the same at all!”
YOU THINK SO? THEN TAKE THE UNIVERSE AND GRIND IT DOWN TO THE FINEST POWDER AND SIEVE IT THROUGH THE FINEST SIEVE, AND THEN SHOW ME ONE ATOM OF JUSTICE, ONE MOLECULE OF MERCY, AND YET— Death waved a hand. AND YET YOU ACT AS IF THERE IS SOME IDEAL ORDER IN THE WORLD, AS IF THERE IS SOME… SOME RIGHTNESS IN THE UNIVERSE BY WHICH IT MAY BE JUDGED.
“Yes, but people have got to believe that, or else what’s the point—”
MY POINT EXACTLY. (Terry Pratchett, Hogfather)
So whose ethics are we talking about? Liberal ethics? Conservative ethics? Western ethics? Eastern ethics? Male ethics? Female ethics? Other-Non-Binary-Gender Ethics? Religious ethics? Scientific ethics?3 When you boil the very complex study of ethics down, all we humans really believe is, "Someone has the right not to be hurt and to keep what they have." And not everyone believes even that.4
So, ethically, what's the right way to raise the child?
The moment what you're doing becomes known to the public, there will be a crowd of well-meaning but under-educated5 people protesting outside your doors that what you did was unethical from the moment you thought of it.
If you raise the child as feral, there will be a crowd of well-meaning but under-educated people protesting outside your door...
If you raise the child with humans, there will be a crowd...
I hope you get my point. Ethics is a point of view. In real life, no matter what choice you make, you're screwed. The only choice you really have is how much effort will be required for damage control based on the choice you make versus the value of the proposed knowledge you'll gain.
Which, of course, is why the U.S. government has been keeping the Roswell aliens secret at Area 51 since day #1. 😁
OK, So what's your Frame Challenge?
You're barking up the wrong tree. You need to stop worrying about what the "most ethical method" is and focus on "what are the ethics of my investigators?" Answering that question automatically answers the first. Unfortunately, this new question is too story-based to ask on this Stack.
1 This deserves a bit more discussion. There's a fairly large field of psychological study concerning human primal behaviors in civilized society. It's an issue right now as, at least in the U.S., we debate what is acceptable involuntary behavior and what isn't. While we can argue until the cows come home whether or not humanity has successfully overcome any aspect of its original, aggressive animal behavior with the onset of intelligence and education, the reality is that the answer is certainly yes. The only real debate is "how much?" Or, worse, "how has the original primate behavior changed to accommodate the influence of education and indoctrination in any form?" Frankly, that debate is going to be going on long after everyone who's using this Stack today is long dead — but we have to boil it down somehow for the sake of effective worldbuilding. So, IMO, the influence of humans raising the child would wash away any effective knowledge you can gain from the experiment.
2 As I said earlier, your problem is that the species must have evolved to the point of cooperative behavior that subjugates the primal behavior to make room for the intelligent, educated behavior. Otherwise it's unbelievable that the aliens got to Earth in the first place. It's nice to think that you'll find a useful tidbit of information (like the cute little aliens on the Beryllium planet in "Galaxy Quest" that suddenly smile with sharp little teeth and eat their wounded pal), but in reality, there will be precious little of behavior like that. Your aliens, like humanity, had to become domesticated to develop the skills necessary for interplanetary flight. That means the only practical differences, other than perhaps noting that they tend to lick their noses like dogs rather than blowing them with hankies, will be cultural, and you can't get to that data.
3 This is starting to make sense, right?
4 If you want to see someone's idea of what happens when you change the "majority opinion" of what's ethical, go watch one of the "Purge" movies.
5 From the point of view of the people inside....