A very simple scenario here with somewhat related background: take absolute pitch for example. I don't think anybody would argue that absolute pitch cannot be acquired, if you are an adult, don't have it already, and set out to acquire it. Some people can achieve it to some degree, but the phenomenon of AP, strictly speaking, is entirely unlike what these people train themselves to do.
There are clear neural signatures associated with people with "true" AP, and to this extent the most likely explanation is that a combination of early training, and biological predisposition, are important factors in AP development. The literature seems to point to 7 years as about the "cutoff" for the "critical point."
Now the thought experiment. It is possible to invent a language that requires AP: we would encode special meanings to certain frequency classes. (this is not at all a stretch, given the existence of several whistle languages). Then, if you pass the critical point of AP acquisition, there is no chance of you learning this language.
Okay, maybe that was extreme, but as we relax the constraints bit by bit (like how rigid the frequency classes are defined), we can create languages that require different degrees of AP ability. In this thought experiment, I would expect a readily observable critical period effect.
Suppose this all follows through -- then, these languages must be learned as children.