In Dramas for some reason, the leads magically meet all the time. And due to that they get to know each other more and after a few episodes, they are already in love. But I don't think it's that easy, especially if they are total strangers. You won't always meet through fate, but instead, might have to ask for dates etc. in order to meet. 

Well long story short, does anyone know a drama where the first few episodes are kinda awkward because the leads can't ask each other out/ make the first move. Like in general pining

I don't know if it fits your criteria precisely, but One Spring Night seems to generally be what you're looking for.  The FL already has a long-term boyfriend when they meet,  so they agree to just be friends for the first 5 or 6 episodes.  But of course they eventually go beyond that.  The leads are both smart and mature, and their conversations are realistic and believable.  It's a great drama, one of my favorites. 

My Unfamiliar Family also has a pretty good late-blooming romance between best friends who take a while to see each other as more than just friends.  And of course there is the classic Coffee Prince, where the ML and FL are crazy about each other but can't have a romance for a long time because the ML thinks the FL is a guy.

 

In Romance is a Bonus Book the leads have been friends since childhood and I thought the slow development of their relationship into romantic love was beautiful and had realistic bumps.

 honey:

In Dramas for some reason, the leads magically meet all the time. And due to that they get to know each other more and after a few episodes, they are already in love. But I don't think it's that easy, especially if they are total strangers. You won't always meet through fate, but instead, might have to ask for dates etc. in order to meet. 

Well long story short, does anyone know a drama where the first few episodes are kinda awkward because the leads can't ask each other out/ make the first move. Like in general pining

Maybe You Are My Glory? The leads went to school together but didn't see each other for ten years after they graduated. When they were in school, the FL used a side email address to create an account for an online forum on space so she could friend and chat with the ML about space (his area of interest) without him recognizing her. Ten years later, the FL uses that email to create a second account on a game she endorses (in her role as a celebrity), and the ML's account on that game is suggested to her as a friend because they were already online "friends" / contacts. The leads don't actually meet face to face until episode three, and the FL has to really work in order to make that happen, and their subsequent meetings only happen because the FL asks the ML to teach her how to play the game better. There are only two coincidences: at the beginning of the drama the ML is introduced to the viewers when a mutual classmate of his and the FL spreads a rumour (based in truth) that the ML rejected the FL (who is now a famous actress) when they were in high school. However, that doesn't result in them meeting or even interacting with each other virtually. Second, after the FL friends the ML and he accepts her friend request (recognizing her as the space forum user and not realizing who she is IRL), he accidentally adds her to a game when he invites his other friends in the game to play a round together. TL;DR there are no coincidental meetings. All of their meetings happen because the FL worked hard to make them happen. 

One Spring Night is the best drama for what you are looking for. C

It doesn't entirely fit but I always thought Her Private Life had some organic development even if it does employ the "knew each other as kids" trope. 

Maybe My Golden Life, it’s a family drama with multiple couples, the story is a bit crazy (maybe not so realistic) but interesting. I liked it but might not be your thing?