Guys I need help

Theres this guy I want to be friends with because idktbh he just intrigues me i guess, he’s generally a quiet guy, I’ve never seen him talk first unless talked to be then he’ll be friendly. he doesn’t seem scary just quiet. I want to be friends with him but I have social anxiety with people I don’t know. I feel like it’s rude just to approach people I don’t know for conversation I feel like I’ll be interrupting their thoughts. also i met him at my new softball team. these are the interactions I’ve had with him:

- I was distracted and he let me know it was my turn

- he asked me if i wanted to warm up passing the ball.

- I was rlly thirsty and forgot my waterbottle so i decided to ask him if there was a bubbler. I was so scared expected him to look repulsed but instead he smiled and stepped a foot forward to hear me and he maintained eye contact the whole time. he has the most beautiful green eyes which I didn’t know. and he genuinely seemed like he thought abt it.

- both our siblings go to homeschool taekwondo class and this was my second time seeing him and there wasn’t many seats but my mom made me SIT NEXT TO HIM, which I’ve never done. he was on his phone the WHOLE time. scrolling. so I turned my head to say hi but he didn’t seem to notice. once he stopped being on his phone his arms were crossed, I felt super nervous, but I sat criss cross applesauce on the chair watching my siblings, and he kept drinking his water and put his hands in between his wide open legs and then shook his leg.

i don’t want to be the super pursuant but I know he isn’t super social so I’m not offended. but I don’t want to feel like I’m pulling it out of him or ask him to hangout right away. how do I establish something and is he even interested? none of these places are a super social time.