How does someone move from being an acquaintance to friend?

I have quite a few acquaintances some of whom I think are actually pretty cool and I’d like to move from someone I chit chat with occasionally to actually being my friend. I feel like through life the friends i’ve made, I’ve basically stumbled on or they chose me to be their friend. I’ve never pursued someone to be their friend. I’m also very shy and overthink things a lot. I fear that i’ll come off too strong or my pursuit will be unwarranted. I really want to foster more friendships.