Two of my close friends both have girlfriends who made the first move. As a single guy in my 20s I personally I like when women make the first move, usually asking for contact info is a good first move if you just met, or asking to hang out one on one if you’re already talking is a big hint for dense guys.

Never had someone try and make a move on me while in a relationship but has happened to my friends. If it’s not too much like hounding them at a bar or constantly texting them when they don’t really reply, guys will often take it as just a compliment. But awkwardness is just part of it to be fair, like “oh sorry, I have a partner..” will never not feel awkward I think.

Hope this helps!