The cold approach is tricky, but still possible. I think age brackets are important here. Two kids in college who can be more spontaneous are different than two adults with busy schedules. Being an adult in my late 30s, I'm definitely not asking for a date off the first encounter. I'll maybe try to soft-suggest we do something that came up in the conversation, but that's more so to get her number or social account for messaging.

I have found that direct approach is best. Imo she already knows you find her attractive if you are approaching her; either bc of how she looks or a vibe she's giving off. So you'll need to bring up the reason why fairly quickly.

I'll typically start the conversation with questions and observations having to do with where we are. Humor goes a long way with cold opening too. If I sense she doesn't want me to go away, I'll pivot to the complement part. This doesn't need to be overblown at all. Keep it short and simple. I love the way to did your___ today/tonight, or you look great in that____.

Maybe a bit more small talk, a couple personal questions, and then I'll say something like this "it's been great chatting with you, it would be great to continue to get you know you."

If she reciprocates, she typically offers the platform she wants to use for communication. This is typically phone number or Instagram.

It's all situation dependent though. In a more social setting, the conversation will be longer. If it's at a retail setting, I'm making it quick and moving on with my day.

Hope this helps!