Culture came first because food and water are absolutely necessary to human existance. When I awake each morning, language is not important to me. Taking care of my basic needs is important to me and while I'm no neanderthal, I can only imagine that the early humans were much like me in this respect. Forget the petty small talk, give me my water, or coffee, etc. As I think of early history as "morning", I realize the awakening of human kind and that most certainly, language developed from culture. Culture is the social evidence of mans need of man and it defies language because it is full of symbolism.
It is the recognition of the past, less in language and more in actions.
Ever notice when men or women, or children, for that matter, chatter endlessly after a triumph of sorts? Whether it be a slamming game of tennis or winning at Bingo? This is where I base my personal theory that culture came first.
The culture of the hunt was no doubt a big part of early humans lives. That culture would have had to involve "hand language". It also involved that part of the brain called, The Central Core where the Thalamus, Pons, Cerebellum, Reticular Formation and Medulla are located. Over time, the hunt required more and more of the Cerebral Cortex where planning and perception take place. Two men, seeing their fellows hungry dragged up a mastodon and shared. Later, the fellows followed and assisted in the hunt.
The Reticular Formation, which signals the Cerebral Cortex to attend to new stimulation was vital in the beginning of language.
So that the culture of the hunt, that actual coming together to get the necessary (food) eventually led to language which was probably an emittance of thanks-giving and cheer. Maybe they began grunting in unison and then began getting each other's attention with grunts. No doubt mistakes were made in communicating with mere grunts and more specific sounds were made for specific objects.
As time wore on and the Cerebral Cortex was more and more "pinged" by the Reticular Formation, words for abstractions such as "herding" or "ambushing" came to be. And the brain blossomed from there as language became man's greatest discovery.
Man then formed words to explain his actions, which may or may not precede a cultural change. Language is now more important than culture as the world grows smaller. But culture is what keeps language important in terms of mans ability to nurture man. Or, cease from destroying himself in the universal sense.
As man evolved in each his own lifetime, culture became ever more important to him as he reflected and realized the importance of remembering. And without memory, language is useless.