Should I approach this guy at the gym that I’ve never spoken to?

Hi all!!

Let me start this out by saying I’ve never dated before. I’ve been scared of it (and men, lol) but I’m trying to get out of my comfort zone this year.

| (25F) have been noticing a guy that I find very handsome at the gym for a while. I often catch him looking at me (then look away) or he looks in my general proximity a lot. Especially the last week or so. He's also been working out in my proximity more often than before and it feels slightly intentional.

However, we haven't spoken to each other yet and if I'm being honest, I probably come off as entirely uninterested. I avoid looking at him or maintaining eye contact and I don't smile at him when he looks at me because I'm busy looking away and pretending he doesn't exist bc I'm nervous. Not the best strategy, I know. however I honestly get the *vibe*

that he could be slightly interested. Or it's my tism.

I know there's kind of a stigma around men asking women out at the gym so I'm wondering, would it be appropriate for me to approach him and respectfully ask him for his number or something? This is new to me and I'm unsure of how to approach this. He's cute and I know that if l'll be bummed if I let this slip past when I could've at least tried. But idk!! Pls help!!