Hello. Lucky Hammy - it's a lovely cage
As Drago says adding a lot more substrate will help - I would put at least 5" in so it's about 1cm below the top of the base. That might sound extravagant, but the idea is that the more substrate you put in, the less often you need to clean the cage. Plus hamsters like digging and burrowing in it and burying hoards in it.
Clean outs are very stressful for them and although pet shops usually advice cleaning out once a week, a lot of people find it's better to just "spot clean" regularly and only do a "big" clean out every 2 to 3 months even. With spot cleaning you just take out the odd handful of soiled litter (which might be not very often at all if your hamster uses the litter tray), and replace it with a handful of new and mix it in so it still smells familiar. They are very aware of changes of scent or everything smelling different. That way you just replace the odd handful occasionally - the bottom half of the substrate usually stays dry. If the litter tray is used just empty and clean out that every 5 days or so and replace the litter (a lot of people use chinchilla bathing sand in litter trays).
So although it will take a lot of substrate initially (you might need 2 or 3 bags of Carefresh if that's what you're using, but there are cheaper similar substrates you can buy in bulk - more about that later
) after that you will use very little for a couple of months or so until you do a clean out. Even then I don't clean everything at the same time, so something always smells familiar to the hamster. So I would do the substrate (I usually chuck the top half, keep the bottom half, or clean half, and mix it in with new, so again you don't use that much at clean out time). A warm damp cloth for the base of the cage is enough. No need to use disinfectant unless there has been illness or disease. Even then only use petsafe disinfectants for hamsters and rinse well to remove any scent afterwards. I then clean the toys a different week and the wheel a different week again. It reduces the stress for them as if all their familiar scent is removed at once it is stressful for them really.
So - re your cage set up
Add more substrate. The little pod houses are a bit small for Syrians to nest in (our last Syrian tried to but the top kept popping off when he stuffed it full of bedding!). Ideally they need a bigger house which is sat on top of substrate and open underneath - so it doesn't get sweaty and smelly inside and so they can burrow down in it a bit and get cosy, plus they sometimes like to keep food underneath their nest so they can snack in bed.
A good cheap option is a shoebox. Cut the bottom out and a hole in the front for the door and it makes a house that can sit on top of the substrate and easily replaceable if it gets soiled. The lid can act as a lift-off roof so you can check inside without the nest falling apart - although that might be tricky in your cage as the house would probably need to go under one of the shelves but lifting the lid off isn't essential anyway.
So how do you have deeper substrate and fit a house under the shelf? Well the house can be partly buried in the substrate and you can just scoop out a bit of substrate where the entrance door is. Your hamster will probably move in and build a nest there. The danger of not having a big enough house right now is your hammy may decide to start nesting in the tubes and block them up, which is not very healthy and difficult to clean out, plus makes their behaviour a bit funny sometimes as you have to clean it out more often then - and it can get smelly in the tubes too.
What a lot of people do with that cage is remove one of the plastic shelves and just keep one shelf in - that gives you more cage space to fit in a house and a Syrian sized wheel. The wheel that comes with the cage is too small. I didn't check on the photos whether you have a bigger wheel or not, but if not, you'll need to get something bigger than the 6" wheel the cage comes with. 11" is a popular size for Syrians and it will fit any Syrian even if they grow very large (which some do!)
Some people also remove the tubes and block them off. That's up to you. If she starts blocking them up with bedding I would suggest removing them and blocking off the entrances (I think the cage comes with caps to do that). If she isn't particularly large and fits through them ok and doesn't block them up then they might be ok being left. But some larger Syrians have got stuck in tubes, especially when they have full pouches as they can be quite wide with full pouches.
For now you could just add more substrate and add a cardboard box house. If you don't have a shoe box then something like a tissue box would do as well.
A lot of people get Fitch substrate. It's very similar to Carefresh - it's just recycled food grade paper. Although it doesn't come in colours, it's just off white. It works out a lot cheaper and hammies seem to love it as it's nice and soft. You can get it in 10kg or 20kg bags. The 20kg bag is huge so if storage space is an issue then the 10kg bag might be easier, although the 20kg bag only costs about £3 more than the 10kg bag! It needs to be stored indoors really or it can easily smell damp or go mouldy stored outside or in a garage. I get the 10kg bag and have it in the corner of the room with a throw over it so it looks like a small beanbag chair
You can still mix Carefresh in with it, or sprinkle it on top, if you like the colours. The Fitch is only available online (unless you live in Cheshire and can pick it up from the manufacturers).
https://www.fitchrecycling.co.uk/ani...-delivery.html
One of those used to last me about 6 months in a cage the size of yours, with spot cleaning mainly.