What’s your advice on how I should do this?

Disclaimer: Where I live, people are free to meet other people. There are 0 active cases of the virus.

There's this girl (22), I'll call her Jane, that I (22) think is very pretty, and I have been told by a guy friend that she is a great person. We have some friends in common, but me and her have never hung out or had a 1 on 1 conversation. However, she for sure knows who I am, she knows one of my guy best friends (she studied with him) and I think she may be into me a bit.

Some days ago I was with some friends in a public park having a barbecue. I was on the grill, when suddenly 4 girls arrived to the park (they weren't with my group). Out of those 4, 2 of them I don't know, 1 is a friend of mine from university and the other was Jane. Jokingly, I asked my friend "Hey, do you want some chicken?" and Jane answered me, thinking I was talking to her, when then my friend answered me and I think Jane realized I wasn't talking to her. She kept smiling though.

So, with this said, I was thinking of asking out Jane. How do you think I should do this?

Since there's no way I can arrange a way to hang out with her with friends, I was thinking of commenting through her DMs one of her next instagram posts or stories, trade a few messages and then say something like "I was wondering if you'd like to hang out sometime at [place]?" depending on how the conversation goes.

What's your advice for asking her out, despite our almost inexistent relationship?