a productive meaning of “impossible” could be “sounds I cannot make with my current equipment”.
Probably worth mentioning that most of us utilize recorders and/or samplers which are capable of recording sounds we hear out in the world, so I’m going to take all recordable sound as “possible” for these purposes. Of course, a recording of a sound is different from the sound itself, in the same sense that the word “tree” is kind of like a picture/representation/symbol of a tree rather than a tree itself. So all sound recordings must necessarily fall short of the sounds themselves in terms of approaching truth.
In the realm of synthesized sounds which do not or cannot occur in nature (as far as we know), I tend to believe that our ideas of what sounds “are” and “can be” are limited drastically by the sounds we have heard so far in our lives. The possibility space of sound is limited to what we have heard, as well as the extremes of pushing discovered synthesis techniques as far out as they can go. If it’s never been heard before and it hasn’t been capable of being created before, our imaginative sonic space in our heads does not, and probably cannot, include it. That doesn’t mean that it can’t potentially exist, however. This is an optimistic view, because for me it means that there are MANY currently ‘impossible’ sounds which would probably completely blow our minds if we heard them and had access to creating and utilizing them. It could very well be that we are primitives still existing in the early age of sound possibility, with woefully limited minds incapable of conceiving what others will take for granted soon enough.
I don’t think I’ve ever heard anything in my head that I feel couldn’t be synthesized to some approximation of accuracy. When I was in high school, I was constantly “hearing” sounds in my head which I had never heard before in recorded music, even adventurous electronic music. But now that I have explored synthesis for 2 decades of my life and have accrued a lot of wide-ranging tools for synthesis, I am fairly certain that I have at least some promising starting points to pursue generation of any sound I “hear” in my head. And to be honest, the older I get, the more I suspect my brain plasticity limits the possibility space of that which I hear in my head. Some people might be fooled into thinking that because they can synthesize any sounds they hear in their head given enough time for the task, they can synthesize any sounds at all. But it’s pure fallacy and hubris to believe so. The problem is that you’re starting with a sample set that’s already limited because that’s the way our brains work - they ruminate on what they’ve experienced, and then create a space for those experiences and all potential combinations of those experiences, and then they live within that space imaginatively. But that space will increase, and indeed has increased for people throughout history.