They'd likely develop a way of communication, but not an entire language. It took humanity between hundreds and tens of thousands of years (depending on which studies you believe) to develop spoken language. One generation would not be able to develop a functional language without learning an existing one for reference.

Emperor Friedrich the Second supposedly did an experiment with children in the 13th century to find out about just that.

Isn't that just terribly gruesome?!?

This has actually happened. They developed their own language. https://en.wikipedia.org/wiki/Nicaraguan_Sign_Language

I would venture that it depends on a lot of factors that would be hard if not impossible to control.

For one thing, what exactly are a child's needs? Naturally they need food, water, and shelter at a bare minimum, but what about social and educational stimuli? There's definitely some socializing that can be done without language, but how much?

For another, communication is more complex than just words and phrases. Body language is essentially impossible to not convey; any experiment would likely be unintentionally contaminated by whoever brought them their food. Vocalizations also aren't all language, like a baby crying; we have a born-in capacity to cry with varying intensity.

I suspect that a group of children raised without outside contact would develop a basic language and culture, but from the outside looking in it would probably look quite a bit like how ape cultures look to us.

This experiment was actually done, I can't remember by whom and I m too lazy to look it up atm, but in the end, all of the children died

As far as I remember one of them uttered a single-syllable word that sounded like it was from an ancient ancient mesopotanian language. They all died extremely young.

If there is less than a sizeable number of people, they will not develop "proper" language. Language is used to transmit information in times of need, desire (or even "wishes", however they might be distinct from desire) or distress. If their "basic needs" are met, this alone creates a paradox: they will never have to communicate about those "basic needs". Also, experimenters will tend to communicate anyway, and also every "experimental situation" will consist of what could be considered "communication". You could simply say that you cannot (ethically?) put people (be they children or not) in a sitation devoid of communication. And whatever situation you're putting these people in, you do so by communicating to them, in a sense, which will distort everything that happens.

There have been instances of "spontaneous language generation" above a certain level. All documented instances were in in front of a background where plenty of people (numbering in the hundreds or thousands) were "accidentally" deprived of the language that was spoken in the background culture. For example, there are many well-developed sign languages (used by those who are hard of hearing) all over the world. They all have in common that a number of people in need of communication, but not having (proper) access to hearing were meeting on a daily basis or even growing up together. Spontaneous "homesigns" developed to a language with complex, *recursive* signing systems.

There even were a few fringe cases, like Helen Keller, who was born blind and deaf, who was *endowed by the surrounding culture* with a specific language (written english transmitted by touch), which she was able to use until her death. Or a pair of danish twins who grew up in custody of a deaf person for some reason, wo invented and developed a language, until linguists turned up and ruined it for everybody. Owing to the circumstances, their langauge was restricted to their experience world, but most interestingly, it featured "names" for the respective other twin. For example, one twin communicated to a caretaker, "(my twin sister) (has/is using) (that wooden playhorse that we're always playing with)".

These two cases together leave room for a hypothesis like: normally, a human is born with the ability to and the desire to communicate. It will attempt to do so. If these attempts are frustrated to some extent, this will lead to a somehow detached state. Whenever a human responds to those attempts, it will gratefully be received, and sometimes this will lead to another langauge being received. Normally, this is the langauge spoke in the environment, and only in extraordinary cases, a "proper" language - a "recursive" one - can develop.

Normally, this recursion is Chomsky level 2 (context-free), but there are many cases that are "complexity on level 1" (like "irregular verbs" - we've got this verb, and for some reason it sounds different in every of our 24 combinations of time and person, and there's even a full-blown register of 24 *other* combinations) or on level 3 (or borderline level 2, like "split verbs" - german can be very curious in that regard), and these appear to make learning a language hard in a way.