At 3 months of age I would wake the 3 month old up at night in the middle of the night for a feeding.
Try to feed the baby in the middle of the night and if they don't want the feeding then they might not be hungry.
Some 3 month old babies go through the night and sleep through the night without needing a feeding while other 3 month old babies may wake up in the middle of the night and want a feeding.
My first baby boy woke me up in the middle of the night crying and wanting a feeding while my second baby boy didn't wake me up at 3 months of age for a feeding.
I did however wake him up at 3 months of age and sometimes he wanted a feeding and other times he didn't.
After 4 to 6 months of age most babies do go through the night without needing a feeding.
If you feed your baby before bed then if the baby doesn't wake up in the middle of the night to need a feeding then they may not be hungry.
Most babies will wake the parents up at night by crying for at least the first 6 months of their lives.
As long as you've fed the baby before putting them to bed the 3 month old baby can safely sleep through the night without a feeding.
With my first baby I was really worried and did my best to make sure he was fed and taken care of but after the second child it became less worrisome.
I still worried about my kids and babies and still do but the worry is a bit less than when you're a parent for the first time.