This is a difficult topic for me to talk about without spoiling things, because your relationships with both Callum and Charlotte are highly variable and potentially very complex. But here are my best attempts:
The short answer
The short answer is that I won’t be adding any more variations of the backstories available in the prologue, because I already have nine of them to contend with and they already all have significant impacts on the flashback chapters. However, the flashback chapters themselves miiiiight provide opportunities to play out scenarios kinda-sorta similar to what you’re suggesting. Maybe.
The long answer
The long answer is that it’s complicated. Charlotte is not one of the revealed ROs, which means the only way an MC can canonically be with her is if she’s the secret RO (which, of course, she’s not, because the secret RO is definitely the Clumsy ArcherTM from the prologue).
If you’re specifically asking if the MC can have feelings for her…maybe? If so, that would be a thing that would hypothetically play out through the flashback chapters themselves, not the predefined backstories described in the prologue (which are more about Callum than Charlotte, anyway).
The specific scenario you lay out about being a rival for Charlotte’s affections and ‘losing’ to Callum, though, would never actually play out that way, because Callum was already with Charlotte by the time the MC even met her. I would maybe consider an “in love with your brother/friend/ally’s girlfriend” scenario, but even then there wouldn’t be much of an overt struggle over Charlotte’s affections, because Charlotte would never cheat on Callum (not to mention she doesn’t even like you, at least at first). Callum, meanwhile, wouldn’t particularly care how you felt about her as long as there was no chance of him losing her, which—for the duration of time in which they’re together—there wouldn’t be.
That all being said: it’s worth noting that Callum’s breakup with Charlotte is unavoidable and will happen regardless of the specific backstory you choose with him—it’s given special focus in the “in love with Callum” versions of your backstory simply because it’s most relevant there, but it will definitely occur whether you play a part in it or not. So in the event that Charlotte does somehow end up being the secret RO, you’d potentially have a chance with her after said breakup.
A lot of this is in vague, hypothetical terms because I don’t want to reveal what is, in fact, possible or impossible, but I hope you understand the gist of what I’m saying—the specific scenario you’re proposing is impossible, but there might be other possibilities that could interest you later on.
In any event: regardless of what ends up happening with Charlotte, don’t worry too much about being left out—your relationship with Callum is significant, but it’s not the sole defining element of your character’s backstory. There will also be other opportunities to pursue romantic interests who aren’t male, if that’s something you’re worried about. (There’s a list in the OP, if you haven’t checked it out.)
Edit: wait why do you want to be with Charlotte when you don’t even know her yet?
