Oh, this is a cool thread! :3 This is gonna be a long one, since I'm super passionate 
I always thought, for the very first Part of Sky Diver, that this song would fit best as the first opening:
For the ending, I once heard this one in a speedpaint and I liked it so much and how chill it sounds, but I was also very young when I found it, so I can't surely say that it would fit with the current plot of the story at this point in time. It is a nice song though, no doubt about that:
And oh boi, I love to daydream a lot about how the later openings could look like, especially Part 4 & 5, which are my favorite parts of Origins!
Context, read at your own risk
Part 4 is a tournament arc which is directly followed by the most gut-wrenching one (for me at least because I'm a little scared with how people might react), because the protagonist will fuck up so badly that her mental health spirals down really badly, like, far south, but the tournament kinda gives her the second chance to prove herself as the true leader of the team and show that you can come out even stronger after failing. Also, there's a huge plot twist in this arc, which is one of the antagonists actually being an anti-hero by being a double-agent, who has their own reasons for choosing the side they're on, but rather wants to fight alone. Last but not least, there's one of the strongest antagonists the team faces, being a huge inter-dimensional organization fighting for the sake of "justice", but in a more forceful way than the teams do it, which is why conflict will arise because the big organization wants to integrate the teams into itself, so they have even more power to control and use for their own benefit.
They do have a common goal, but instead of control and order, the 5 teams stand for freedom and a little bit of positive chaos.
And this is almost the spoiler-free version of Part 4's plot lol
I imagine Part 4 to have an opening similar to this one, because I like the interpretation I once read about the name of the song, being that graphite & diamond are similarly hard materials, which really reflects how two sides are competing against each other.
For the 5th and final Part of Origins, I thought of something like this:
Big spoilery context again
This one can be interpreted as a training arc, but there's more to it, since the strongest members of the Sky Diver's really go all out with what they do, facing their fears head on and eventually fight something that is considered above gods in terms of power levels, earning their place on top - which finally gives them the title they hold in the introductory episode: "The legendary team Sky Diver"!
