It is absolutely possible for a trivial reason: everyone does it.
When we are young, and learning our first language, we absolutely don't understand the perspective of the adults speaking around us. Yet 100% of us learn to speak our native tongue.
The trick is that you have to actually learn the language. In school, we often kinda-sorta learn a language. We learn to map it to the way we think, word by word. As you point out, that can fail when we try to learn a language that groups things differently.
To learn such a language, you have to learn it as it's own entity, and slowly develop your own translation over time. One place I've had to learn this is in learning Chinese martial arts as an American. I'd say some of their concepts don't map 1:1 to English, but I'd be lying. Of the important concepts, almost all of them don't map. They simply view the nature of life (and thus combat) differently. It is almost completely impossible to learn concepts like Yin, and Yang, with their proper constantly-entwined-opposite nature just through lecture, much less pointing at things. Concepts like Chi are even harder; Shen may be hardest of all. (disclaimer: still trying to get a handle on that last word, myself!)
Such difficult terms are taught through interaction, not just one way communication. Not only will the teacher use terms like "chi" in their instruction, but they also observe your actions and strive to identify moments where their terms may be more meaningful to you. You may be struggling with tension at some point in a posture, and the teacher realizes that you "know" what to do, you just need a nudge. They might, in a commanding tone say "use the chi!" and that tone alone nudges you into doing what your body knew to do all along, you just weren't doing it. You then start to associate "chi" with the particular correction you just made.
Over years of practice, you eventually will develop your own understanding of the word and tie it back into your life. I, myself, have concepts of what "chi" is which stem from my scientific background, but that's only because that's a convenient way for me to think about it. I prefer to think of it as its own concept, and not translate it into scientific thinking if possible. That way I can continue to understand the nuances which I might miss if I assume that my scientific definition of chi is the definition of chi.
SO I would say the solution to this problem is interaction and persistence. Not only should one be trying to learn the language, but you should try to let them help you find situations which make it easier to understand their language. As they say in language classes, you'll know you've got it when you start dreaming in their language.
The hardest words to capture in this way would be those related to the warrior spirit or the fundamental essence of a society. The former is tricky because you must be put in stressing situations to uncover it, and the latter is tricky because you aren't them.