Approaching a girl in public should not be seen as creepy unless you're doing something objectively creepy. It sounds like your insecurity talking and if you're insecure about approaching then you'll fail any shit test about your approach.

I've walked up and sat down with random people for the heck of it and it usually turned out well. If you do it with a confident mindset I imagine you won't have much trouble but you have to put yourself out there with the possibility it'll go nowhere

Alone on a bench, I'd say no. They've purposely gone out of their way to sit there, and it would be awkward. Rather than that, I would just say "Hi :-) That looks like a nice spot to eat lunch" and then keep moving. Practice opening always, but you don't need to hang around. That's just uncomfortable making.

For the girl sitting alone at a table, absolutely go up and sit down next to her, and say a nice big hello, with a smile. Wait a moment. Then make a comment about how beautiful the day is, or some other observational comment about life, especially anything happening in the present moment, something that would draw her in. These kinds of tips are bordering on PUA thought-process. E.g., making observations, Demonstrating High Value, but they are important social strategies for building rapport. Sitting down next to her and then being stoic is going to seem really weird. You've got to be the fun-loving "I love people" kind of guy, who just wanted to sit next to another person to shoot the shit with them. At some point, you can pepper the conversation with something a little pointedly sexual if you are man enough. Something like, "Nice necklace. I like the way it draws attention to your breasts." Hold frame and eye contact. She'll blush and turn away. Then you diffuse the tension by saying something de-escalating. Eg., a false disqualifier, or just a change of subject. E.g., "Oh my goodness, look at that!" Again, I'm getting too into specifics here. But the point of it is to keep changing the subject, keep owning the frame as the confident, socially outgoing, interesting and interested dude, who's not afraid of expressing sexual interest, but who's also not hanging around waiting for a response from her. She's totally invited to not respond to your advances in any way, at least for the first few hours that you're interacting. After that, if she hasn't reciprocated any of your advances, then she's not interested and you move on. By then, maybe she'll have some friends for you to meet. Start out as if you're just trying to make friends, but that you are simultaneously a hot-blooded male. This reply is too long already. Good luck.

Never approached a girl, you're social awkward??? Youbare thinking about a cold approach sitting at a lunch table whoch could last up to 30 mins, NOT a good idea.

Approach people in passing, hey, what did you think of thay exam? Blah. Blah, blah .ok, cool ttyl BYE...just get through those obligatory hey youre in my class type convos...they'll help