Is there an avian vet in your area? They should have an incubator that you MAY be able to borrow, if it isn't already full to the brim!
Failing that, I'm afraid you'll just have to wait for your incubator! You can make an incubator yourself, but keeping a space at a constant temperature for 4 days will be almost impossible without a bit of specialist equipment such as a heat pad and thermostat.
In a day or two, your bird should lay another egg - maybe it would be worth trying with that one?
Now please be aware that hand-raising a bird, especially a small bird like a green-cheek, will be very difficult, time-consuming and trying. It could end in disaster - are you prepared to see a small baby bird die, and know it was your fault?
I'm not sure what type of incubator you bought, but cheap incubator - suitable for chickens and ducks, may not be good enough for a parrot. Precise temperature and humidity control are essential, and if the incubator is not automatic you'll have to carefully turn the eggs yourself, a dozen times a day or so.
If you really are determined, go out to a good library, an avian vet or a good internet retailer and buy/borrow a book on avian incubation and handrearing.
"A guide to incubation and handrearing parrots" By ABK publications is a very good book, but I'm not sure of its availability outside of Australia.
Talk face to face with someone, a breeder or vet, about techniques such as candling, syringe-feeding and banding.