When I was a lad the folks used to get appliances delivered in big boxes that I used to then spend days playing in… they now don't seem to package things like they used to. My local appliance store confirmed this and said they didn't have any.
Surely they are around though… where would be the best place to try for a big box these days?
my last water heater from bunnings came in a big box. (3 years ago)
Microwave?
Storage box? Some local buy swap sell Facebook groups always have people offering moving boxes.
Ask on your local buy/swap site on Facebook? We got our dryer from Aldi in a big box and have had a couple of others over the years from other random things and they're a pest to get rid of - so you might find people have one sitting around in their garage they'd be happy to give you.
Furniture shop? Last time I picked up furniture they had a lot of big boxes in the skip outside. Mostly big flat ones though, but you could tape a few together.
also a good source for free bubble wrap.
What you need are washing machine boxes, they still come in cubby house format.
Make sure you use good quality packing tape on the boxes, otherwise the kids tend to escape after 10 or so minutes.
Bunnings? I have grabbed a few big boxes from there in the past.