I have a romance arc as one of the major series-long plots of my story. In the first major story arc, the two romantic leads aren't actively together as a couple, this part of the story focuses on when they first met to the point where they realize that they have mutual feelings for one another. Essentially, they both have crushes on one another, but they don't even realize it at first and the two aren't aware of how important each is to the other until the climax.
However, I am having difficulty characterizing the early part of their relationship when their feelings for each other are not overt to sell the sexual tension between them. As a result, the two characters seem to jump from being relative strangers to both being aware that they have mutual feelings for the other. They just seem to "fall into" a relationship rather than have it develop naturally. Making it harder is the fact that a third party, a female best friend, seems to develop potentially romantic chemistry more naturally with both of them than they do with each other. The big issue is the two leads have to be aware of their own unrequited feelings for each other by the climax in order to make the first arc's climax and the broader plot work.
I've been trying to avoid "love at first sight" tropes, not only because I find them frequently unsatisfying from a reader's perspective but also because the genre I am writing in has an issue with poorly written "love at first sight" plots. However, I also know that many techniques authors use to characterize sexual tension between characters have been criticized for being creepy or sexist, for example the recent depiction of Flash and Iris West in the Snyder-cut Justice League.
The novel is written in third-person limited, so it's not possible to give the reader a look into the character's heads to see what they are thinking and thus clue them in that there are feelings going on.
Adding to this difficulty is that the girl is a stoic who is oblivious to social cues and barely even understands her own emotions on a good day, whereas the guy is very shy and introverted (and is somewhat intimidated by her) and so is unlikely to try wooing her in a traditionally masculine way (read: by acting like an idiot). I can't use the cliche of them bickering because they like each other because that's not the kind of relationship they have. I think this is part of the reason the female best friend comes off as having a developing relationship, because this character is more extroverted and hence it is easier to read her actions as being driven by subconscious feelings.
The two leads do seem to have some chemistry together, writing later scenes for them they seem to do rather well together, but the problem is if I cannot establish that chemistry early on and get the characters over that hump it comes off as me retconning them into having good chemistry rather than writing a satisfying relationship.
I know there's a lot of questions about how to write romantic relationships on this site, but what I'm specifically wondering about is how to bridge the gap between very early stages of the relationship, from when people first meet as strangers to when they become aware of their feelings for one another. The broader problem is I am trying to figure out how to depict and write two characters with a crush on one another, both before and after they realize they are in love but before they actively try to attract the other and am coming up blank. I can't even draw on my own experiences because I've never been in that situation myself. I honestly don't know how people with a crush on each other act.