Ah, to be a cat! They don’t have to go to work each morning. They get to sleep all day. If people led such lives perhaps we would be interested in playing at 4:30 am as well. But for working people there is no doubt about it: a rambunctious kitten is not very amusing in the wee hours.
Actually, the problem runs slightly deeper than work-related sleeping patterns. Cats are instinctively crepuscular. This means that they are most active at (and for a few hours before and after) dawn and dusk. Humans are diurnal. We are generally daytime creatures.
This conflict leads to one of the most common complaints I hear from cat people: their pet wakes them up when they want to sleep.
Unfortunately, struggling to make your cat or kitten sleep through the night is fighting against nature. It is often a losing battle. Nonetheless there are some tactics you can employ.
First (this isn’t a tactic, but it might offer some consolation), remember that kittens are more playful than adults. Mature cats are much less likely to become rambunctious in the early hours. Your kitten may outgrow this behavior over time.
Also, remember that truly tired animals sleep longer than those that aren’t. Physical activity and enrichment activities during the day may help your kitten to sleep more soundly at night. Try wearing him out by playing with him each day. But be careful about roughhousing just before bedtime. This may backfire and result in a riled-up kitten when you want to sleep.
On busy days, you may want to consider using a foraging ball to feed your kitten. These devices release food slowly over time as animals play with them. They are excellent enrichment devices.
I have a hunch that if you employ these tactics and wait for your kitten to mature, the problem will resolve. But that’s easy for me to say–I’m not the one being awakened every morning!