I think it's normal at first! She shouldn't be able to escape from her cage though. Do you know how she is doing it? They can open doors sometimes! A peg or a bulldog clip on the door might be necessary before you go to bed. Other escape routes are external tubes (which can be pushed apart), bar spacing that isn't narrow enough, or even a hole chewed in the cage base which you may not have noticed. So it's important to secure her cage.
If it's when she's out of the cage then it might be an idea to set up a secure area like a playpen area. You can buy things to create a playpen or you can make one out of large pieces of cardboard or correx/coropolast held together with bulldog clips (I've had one of these and they're not completely escape-proof so you need to be there and keep an eye on what she's doing - eg chewing it or pushing corners apart.
Also important not to clean out too much as that stresses them and makes them want to escape! Full weekly cleans aren't necessary. A good option is to use a dish as a litter tray (put chinchilla bathing sand in it) and put it where she has chosen to pee - ie her pee corner or area - assuming it's a syrian hamster! Dwarf hamsters tend to pee wherever but only very small amounts. And to have a good depth of substrate/litter - at least 3 to 4 inches - more is better.
The more litter is in there, the less often you need to do a full clean out - you can just "spot clean" ie take out the odd handful now and then and replace it - the bottom half of the litter tends to stay dry. So you shouldn't need to do substrate changes very often - I go two months or more using a litter tray and spot cleaning. Even then it's best to only do "partial" cleans. eg litter one week, wheel another week and toys or house another week again - and not throw her nest and hoard away (unless they're pee'd on and then replace the hoard with new food in exactly the same place, try and leave a bit of the old nest behind and put new nesting paper out).
They don't see well and find their way around by scent - they scent mark things in the cage and leave scent trails on the substrate. So if you remove all their scent at one go they feel lost and get stressed. They are particularly protective of their nest and hoard and removing those will stress them (and encourage them to pee on the hoard to deter predators and thieves!).
So less is more with cage cleaning and it's not necessary to use disinfectants unless there has been illness or disease - warm water or soapy water rinsed off well is fine for a cage base as and when you do a substrate change. Scents and perfumes also affect them and can stress them due to their strong sense of smell and predisposition to chest complaints. So dust is bad and perfumes/scents aren't good (eg in cleaning products or litter). Litter should be dust extracted (on the bag) really. You can usually tell if it's a bit dusty - if so there are alternatives.
Plain white toilet paper is best for nesting - tear it into strips and put a pile in the cage and she will take a piece now and then to line her nest.
Other things that can stress them - if a wheel is jammed and not working, or a water bottle is jammed and not working (the water needs changing every day so check it's letting water out ok then).
No need to worry at night if the cage is secure
And providing there are no fall risks - if a cage is taller than 35 to 40 cm there can be fall risks. Deeper bedding can cushion falls and having the cage set up so she couldn't land on anything hard or sharp if she climbed to the roof and dropped.
A shelf they can sit on or under and a house big enough to build a nest that's dark inside also help them feel secure.
Which country are you in?