Baby no longer showing hunger cues?

Is that normal as babies gets older? My son just turned 3 months & recently discovered his hands. Now he always has his hands in his mouth. Before it was his hunger cue, but now when I try to give him the bottle he doesn't eat he pushes the bottle out with his tongue. My last feed was 3 hours ago. How long can a 3 month old go between feedings? FTM here. I thought parenting was suppose to get easier? It seems that every week our babies throw us, parents, a new curve ball when we think we've finally got the hang of things. 😑