When do babies develop reflexes?

Born with them. Babies are born with reflexes. They turn their head toward whatever stokes their cheek looking for breastmilk. We can suppress reflexes over time but they are something that we are born with.
See below. Babies are born with reflexes. The rooting reflex, and plantar reflexes, are two examples.
At birth. These reflexes include the moro or startle reflex, rooting, sucking, stepping, walking etc. These primitive reflexes will go away on its own by about 4-6 months old.