How do you actually get past the initial wall of approach anxiety in low-pressure settings?

I’m 23 and really trying to step away from relying entirely on apps to meet people, but the sheer initial nerve-wracking mental barrier of cold approaching in everyday public settings (like coffee shops, bookstores, or casual campus spots) is holding me back.
It’s not even about needing a smooth pick-up line—it’s the internal hurdle of breaking the ice without coming off awkward or out of place.