Babbling is a genetic inheritance for the human species only--no primates allowed.
Babbling occurs after that time when, as Luria suggests, the brain has gone through its re-organization. Modalities now work in consort, two at a time.
Hence, the noises that the baby makes are now correlated with the vocal movements that are producing them, and the baby revels in this awareness.
This particular aural circuit, however, is unique only to humans. Other primates do not engage in this activity. Nor do other primates develop speech.
All during this period, the production of sounds increases in frequency and variety in terms of consonants (from back to front) and vowels (from front to back).
The sounds, however, are still relatively reflexive or by chance and do not reflect any language background. The initial babbling is personal and occurs usually when the child is alone, usually before or after a nap. There is lot of cooing and chuckles.
NOTES: Here are some more milesones.