A.S.
Hi S.-
We had almost the exact same scenario, and it does get better. Just when you think you're getting used to sleeping patterns, another one emerges!
It's pretty normal for a 3mo to wake up that much. Babies have sleep cycles where they sleep heavier and lighter at different times in the night. Also, when he wakes up, he might not be hungry. He could be cold or have a stuffy nose or a wet diaper.
Most peds. recommend introducing solids between 4&6 months. Cereal in the bottle can be a choking hazard, so make sure you're watching him if you chose to do that. Good Luck