When your tamagotchi is asleep, don't put it on pause leave it off. Then in the morning when its awake, (Adult tamas wake up 8.00 AM 9.00 AM or even 10.00AM.) the baby will be gone. But you must know when your tama goes to sleep and wakes up.
(Don't blame me if this doesn't work or your tamagotchi dies)
And if it doesn't work your tama is probably too young.
Adults don't leave the baby tamas on their own straight away
Your adult will usually leave the baby at midnight on the second night after the baby arrived:
example; if your tama had the baby at 4pm on a Friday afternoon, the adult would stay with the baby Friday night, and all day Saturday... then it would leave the baby at midnight on Saturday.
Your baby wakes up on Sunday morning crying and as soon as you give it a name you are off with a new generation