How can I keep baby dinosaurs alive?
Solution 1:
Baby dinos in ark need to be fed by hand until they reach 10% growth. They have low food capacity and starve extremely quickly as you have noticed. You need to put the food into their inventory directly for them to eat.
Make sure you have food available and don't incubate eggs if you have anything else to do.
Once they reach 10% maturity they will enter juvenile state and can eat from a feeding trough like all other dinos.
Here is the relevant section in the ark wiki.