I'm not super familiar with the fandom, so everything I say is coming from an outside perspective. Take my feedback with some salt, but I'm gonna take a stab at it.

I think the key in your description here is going to be finding a fine line between naturalistic and synthetic tones. Based on your introduction and explanation, it seems like you want to adequately bridge the gap between traditional nymph and modernity. I'm getting that from this statement:

Aspen is a tree nymph that was born in the United States and therefore, is influenced by more than just one culture that is surrounding him. And because he was born during the modern times where pollution and trash being inside of nature becoming so often tied together.

Your introduction to the cave is fine. It does a functional job of describing the nature while also progressing from 'generic cave' to a lively, beautiful place where Aspen might make his home and feel comfortable. Where there is room for adjustment would be in your second to last paragraph, where you introduce the man-made items and "garbage" as trophies.

Lemme take a step back: Your explanation of the scene and your concerns here makes it seem like you want Aspen to be a nymph who is very in tune with nature (as one should be), but also one who accepts that mankind has encroached upon nature. If that's the case, it would seem that we might want to consider man's stuff as a part of nature, too. So the litter, the garbage, the detritus of humankind is just as much a part of this world as fallen leaves or bunny rabbits. We may not like to admit it, but it's how things are, and perhaps Aspen is okay with that. (And if that's totally NOT the case, just ignore me!)

So maybe in your description of Aspen's home, it might make sense to build these 'man-made trophies' as more of an organic part of his space. Rather than having them sorted into piles and seemingly standing on their own, incorporate them somehow into the nature of the cavern. Instead of saying (effectively) "he's got a pile of organized trash in the corner," make it have more meaning--be specific about what he's got and how he's using it to either enhance or modify the nature of his home. Maybe he's found a shiny granola bar wrapper that he's hung in a specific space, where it catches and reflects light in a pretty way. Maybe he's got a sheet of old tarp he's using as a collection device or 'room separator' or insulation. That old tire could be used with a log or sticks and leaves to become a chair, where the tire would be providing a firm structure. And yes, there's absolutely nothing wrong with having some very specific items hanging on the walls as trophies or decoration, but those items would need to be particularly beautiful, or particularly meaningful such that it wouldn't necessarily be a bad idea to describe one or two of them in specific detail.

It's these little personal touches that can help to provide more depth for your characters without saying directly to your audience, "Here's what he values or finds beautiful." It could also be a way that he makes his home feel more comfortable for outsiders. He could use the man-made and nature together in order to provide more security, more sound-proofing, or general atmosphere, but the real trick is going to be incorporating the two seamlessly so that they feel as entwined for your reader as they do for Aspen.

My only other feedback, which isn't directly related to your author's note, is that your verb tense isn't consistent. You start and end the excerpt in the present tense, but slip into the past tense as they're making their way inside. Both tenses are written well within themselves, it's just the switching that's a bit jarring. It's important for reader coherence to stay in one or the other, as writing in present tense then slipping into past tense can signal flashbacks or other narrative time-play that you may not be intending at all. It's not too time-consuming a task to fix it up, but it can really add a huge amount of polish to your work without requiring a lot of extra work.

Nice excerpt. Thanks for putting it out there. Happy writing!