@kml, that’s been my experience with random pick-ups as well. I remember a decade ago working up the nerve to ask out a cute woman who walked her dog in my neighborhood. She said yes! On our first date I learned she was “sorta” in a relationship but wanted out, my kids were a dealbreaker for her, and we had very few interests in common. I remember resolving never to do that again.
At the climbing gym is a good idea—you have at least one shared interest assuming you’re both either top-roping or bouldering, and the pauses between attempts give plenty of time to chat and assess compatibility before you make a move. If you always come at the same times, you tend to see the same people, too.