I'm not an engineer, but have you figured out where the water will go if the liner (I assume there will be one, so the water doesn't seep away) breaks and it gets warm? Neither your parents nor your neighbors may particularly want a flooded garden, garage or basement. And eventually, you'll have to drain it, or you will get mosquitoes and such.
You could use a LOT of fill dirt - but you have to haul and spread. Let us see - 30' x 60' x 1' average = 1800 cubic feet. Assume a density of very roughly 3.5 - if you are good at math, you can show that it is about 196 tons of earth to haul and spread.
My best guess is that if the weather is cold enough to freeze ice, the ground is too hard for your average lawn tractor to level the ground, and doing it with a hand trowel and a little red wagon would take longer than you have. In fact, doing anything with frozen ground or fill dirt is going to be a lot harder - an engineer might tell you to wait till summer.
If it is level, you could put a fence around and flood your driveway, but your parents might disagree.
You could flood your neighbor's driveway, but they might disagree. Especially after it leaked into their garage and basement.
Also, is there level ground nearby (like a neighborhood park) that is more level that you could get permission to flood without consequences? It might be easier for several neighbors to do this together than one.
You could dam a small stream, but there are a lot of potential complications, along with ecological issues, and you have to time everything right.
BTW, an ice rink is an "attractive nuisance" that can lead to lawsuits, if people can get to it and get hurt.
I've often thought my own rink would be fun. But rinks, especially outdoor rinks, need maintenance, like ice surfacing, if they are to be and stay slippery, which adds a lot to the time and cost.
So - I hate to give you a downer, but this is a big project for a kid.
It seems like a lot of time, effort and money if all you have left is several weeks. Could it be cheaper to hire a taxi to take you to the nearest rink or shallow pond? How about if you estimate the costs of hiring a mini-dozer and an operator, and show your parents how much they save by taking you to the local rink.