Step-By-Step Solution (From OP)
Hey, questions have been raised in comments about me giving a step-by-step answer to this, so I am. This solution will also credit the people that figured out each step.
1. Orienting the Cube
So, what we want to do first is at least find some sides' relation to each other. @AHKieran discovered that sides 1,2, and 3 line up to create a number 2 across the corner, and @Dorrulf noticed that that was one of the final numbers in the code. Also, sides 4 and 5 line up to create an arrow pointing at side 4 (which we'll get to later)
2. Side 2, 3, and 6
@gabbo1092 was the first to find that side 2 was the word CODEX cut in half, as demonstrated here (excuse my bad editing skills):
Now, if we find the letters of CODEX on side 3 (as also discovered by gabbo1092) we get a color pattern: red, blue, black, green, red. Dorrulf realized that if you traced the shape formed by the letters, you get a 7, as illustrated here
which is another number in the passcode. Two down, two to go! Now moving onto side 6, gabbo1092 saw that the color pattern (red, blue, black, green, red) entirely matches the color pattern of the number 4 on side 6. So, we have three of our numbers: 2, 4, and 7.
3. Side 4 and 5
First of all, gabbo1092 saw that it was possible to move the blocks on side 5 to match the position in side 4, following the arrows, in the intended order, by sliding the block on the bottom left, then the vertical one on row 3 down, then the horizontal one on row 2 right, then the other vertical block down and finally, the last block left. Dorrulf then saw that, if you copy the movements (left, down, right, down, left) with a physical pencil, you get the number 5, as shown here.
4. Side 1:
We're almost there. gabbo1092 pointed out that the graph diagram on top of the four numbers corresponded to the size of the numbers, with higher up points on the graph corresponding to higher numbers. The order is second lowest, second highest, lowest, highest. Using this with the numbers we have (2,4,5,7) gives the correct passcode of 4527!
5. Inside the Puzzle Box
Inside the puzzle box was 100 bounty, which will be rewarded to @Dorrulf for being the first person to completely synthesize and present the correct answer. The bounty will be awarded soon!
Overall, this is one of my hardest puzzles that was solved, and I was really excited to see the community work on it and solve it together. Thanks, everybody!