Just googled the cage as well
It is very small and I think you're right to change it. My first thought is - take it back and ask for a refund. A number of people have done that after buying a cage that wasn't right and saying it's too small, too tall or whatever. I think people have had good results doing that with pets at home, even if the cage has been used, and one member said they would wait until she had a replacement cage before she returned it.
Depends where you got it from maybe, but it would help towards the cost of a replacement.
For a Syrian I think it's quite hard to find a bin cage big enough. The RUB boxes mentioned are good but not that cheap and the largest one isn't as big as some 80 x 50 hamster cages (I think).
Sometimes it can work out cheaper just to buy an Alaska cage from Zooplus (about £33) rather than a bin and the bits and pieces for making a bin cage.
Depending how much space you have, a detolf could be an option for a diy cage as well. It's £40 but needs a lid making out of strips of wood and mesh. It's an Ikea glass cabinet tipped on its side with the door left off.
DETOLF Glass-door cabinet Black-brown 43x163 cm - IKEA
Some set ups in detolfs here
https://www.google.co.uk/search?q=ha...BTDugQ_AUIBigB
Personally I would try to get a refund for your current cage and get an Alaska cage. It has a nice big front door for good access and that can help with taming as well. It is not a really tall cage but the height is better if you have plenty of substrate in the base. It's a good size for a Syrian hamster. It doesn't come with much. A shelf, which is apparently a bit flimsy but people tend to find it ok. The white cat house is no good as a house and the holes in it are too small for some syrians so they could get stuck, but it's easy enough to remove it. So you'd need a wheel and a house and presumably you've got some toys and chews already
A good house would be a shoebox house, so doesn't have to cost anything. You turn it upside down so it's open onto the substrate and cut a hole in for a door - it could go well under the shelf or partly under the shelf. Or if you have it in an open part of the cage, use the lid of the shoebox as a roof to lift off and check inside and cut the bottom out to be open onto the substrate.
A popular wheel for Syrians is the 28cm Trixie wheel - also sold by Zooplus if you did get the Alaska but not called a Trixie wheel. You wouldn't pay postage for the wheel if ordered at the same time as the cage.
Alaska cage
Alaska Hamster Cage | Free P&P on orders £29+ at zooplus!
This is the wheel (28cm version)
Small Pet Exercise Wheel | Free P&P on orders £29+ at zooplus!
Another option could be to look for a used Hamster Heaven on ebay or gumtree. They're also a good sized cage for a Syrian and a bit easier to set up as it's a fairly low cage compared to some. Although personally I found that size a bit cramped for a syrian with their large toys and wheel and the Alaska is probably better proportions, size.
I would definitely try and get a refund for your current cage though - if you haven't had it long. It can feel awkward asking, but it's worth a try. Just say it's not suitable for your Syrian hamster.