Well, good to know that no actual practical advise comes from this place when one actually needs it
Difficult for girls to write first unless you're a 10, you're a famous person and you have a profile with thousands of followers.
But you could improve your profile.
First of all you must have some photos of you, possibly photos that say something about you, for example if you travel a lot remember to always take photos, so that a girl can think that you are an adventurous person.
If you are sporty or go to the gym you could post a story where it shows that you are working out so that a girl can think that you like to keep fit.
I can't think of other things, tell me what kind of person you are, what you like so in my small way I can help you.
My Instagram profile is nothing special, I'm good at jumping rope and I posted a couple of videos, I have some pictures I took when I traveled and I posted them.
Someone said that having good photos is enough to impress but remember that chat is also important, you have to try to intrigue her