It ttakes it's time. You should make a mental note:
When your tama is born, it takes two whole days before it grows up.
The best thing is to have a baby in the morning. When your tamas mate and have babies, they usually leave in the middle of the night, so when you see that there's only one moving Z in the screen, try not to wake up the child until the morning. That can make them be grown ups faster.