How can I meet with a girl that I only see in public and is always surrounded by people?

Let me explain the situation in a few sentences:

There is a girl that I saw at my college’s cafeteria a couple of times. She is an Erasmus student and they generally tend to hang out with other Erasmus students here.

She always seemed to be in a girl group made up of foreign students.

I really want to meet her, but how can I do that? We have no common classes, and I have zero knowledge of any potential social circles or events she may attend.

So, it seems like a cold approach is the only possible course, yet the fact that I only see her at the Cafeteria and she is in a group of foreign students whenever she’s there makes it pretty hard. I am normally not a bad talker, but when it comes to something like this, I doubt I can make it smooth.

I know I have nothing to lose, but I don’t want to make things uncomfortable both for her and myself. If you had any advice to give, it would be really appreciated

Thanks for giving it a read.