My cat has a basket of all sorts of toys. During the day, she will not play with them at all, and I know this for a fact because she takes them out and their scattered around my home. But around 3:00am to 4:00am when it's completely dark, I happen to wake up; and her toys are scattered everywhere. She's been playing with her toys at this time for quite some time and I wonder why it's only around this time and not during the day?
It is because cats are most active at night and during the day it mostly naps and is not very energetic. Also at night the cat can see what looks like a mouse or prey, while during the day he can clearly see it and doesn't bother to chase it. Another reason may be that he just enjoys playing when no one is around, like at night, or his hunting skills usually perk up at night. I hop this was helpful
Cats prefer hunting in low light conditions and you might also be entertaining her during the day (with food, attention etc.). If you would like to encourage her to play on her her own during the day I suggest closing the blinds in her play room and turn the lights off. A bit of catnip would also assist with getting her to change her routine.
Cats have well established routines.
Cats love to eat, sleep, cuddle and play at the same time of each day. Therefore, if she allocated 3 AM to 4 AM for playtime, she will play at that time every day.
Contrary to the common knowledge, cats are not nocturnal but crepuscular, meaning that they are more active at dawn and dusk than any other time period. If your blinds are open at night and some street light illuminates your room, she might believe it is dawn and construct her routine accordingly.
In order to change her routine:
Close the blinds at night. Make is as dark as possible so she can't see properly. They are less active in pitch black.
Tire your cat before you go to bed. Cats are very fast and agile but stamina is not one of their good qualities. Making a cat jump several times to catch a string would tire her out for hours. To give a further incentive to play, get a catnip toy and give some treats after an adequate playtime. Note that cats only focus to hunt for five minutes, i.e., they will give up if they can't hunt in five minutes. This means that their attention span is limited to five minutes and you have to wait some time after five minutes of play time or change the game to help her focus.
Before you go to bed, give your cat soothing petting. Some cats love to be "manhandled", some enjoy rough chin scratches, yet only offer light touches at night. This will goad her to sleep.
Once her routine is changed, she will allocate a new time slot for playing alone.