I think I could adapt to trains or flight paths more easily

You also need secure locks. About 95% of burglaries happen in the first floor.

Bummer.

Yeah, I used to live in the basement apartment. Had to use earplugs to get to sleep. Then my ears started hurting when I would lay the side of my head against the pillow. By then the noise would subside. It wasn't all bad, it was cool in the summer. Maybe try ear muffs too. Good luck.

Speak to the adult(s) in the upstairs apartment about it? They can probably explain it to the children better. 5:30 am is well inside commonly held quiet hours, after all.

I find that reminding kids that their floor is your ceiling sometimes will make them a little more respectful of unnecessary running and stomping, if given the chance to imagine if the tables were turned (or floors in this case.) Hopefully you will be able to befriend the girls and get them to feel kindly and courtesous toward you by checking their excess noise.

I am bothered from time to time by my neighbors upstairs, and I've learned to use "white noise" in the form of fans, noise machines, even running the dishwasher and laundry specifically during the high noise times helps. Listening to lectures, podcasts or audiobooks with earbuds helps too - when it's really bad I go for a walk until I calm down and/or the source of the noise is either gone or sleeping.

Bose makes great noise canceling headphones, pricey but worth it.

Is it noise from people walking across the floor, or worse?