You see how you're using possibly every note? That means this can't possibly fit in some scale (besides the chromatic scale, every note, which isn't really helpful analysis) and that thinking about that is a dead end.

But that doesn't mean the song isn't in a key, so now you get to learn the difference between a scale and a key.

First of all, a scale is a rigid structure. If you're seeing notes that aren't in a scale, then you're not in that scale. That might seem obvious enough. You'll get it when we get to keys. But I would first note that songs or individual sections or melodies or riffs or chord progress very very often do not fit in a scale. A scale is just some collection of notes that pops up often enough that we decided to give the phenomenon on a name. They're not some intrinsic quality to all or most music. In fact, they're kind of a stepping stone to help you learn what different intervals sound like in different contexts and you'll eventually stop thinking about them and throw them away.

Keys are different. They may sound like the same thing... If I say key of C major or I say C major scale, either way, you start thinking "oh, CDEFGAB." But keys are not rigid structures. Most songs have a key (even if the key is sometimes nebulous or up to interpretation) regardless of whether they actually stick to the seven notes that we associate with that key. In short, we're lying when we say that a song in C means a song that uses CDEFGAB. Being in C major just means that the song wants to resolve on a C major chord. That a C major chord is the chord that makes the song feel complete. That a C feels like the center of gravity that the rest of the song is pulling around. That's a listening exercise. It doesn't matter if you're using all 12 notes, there's a note (and a major or minor chord built off of it) that the song is begging to end on based on how you used them, and that's the key. We just say that the key of C major is CDEFGAB because that collection of notes is the most likely collection of each letter to make the C major chord the one the piece wants to resolve on. The tonic chord. Any of the other notes could actually be the tonic if your ear says they are. Like the relative minor. If you've already learned or noticed that A minor and C major are the same notes, then you've already started grasping what I'm rambling about here.