It's the old 'which came first, the chicken or the egg' question, isn't it? Absolutely not. Culture is the origin of language, but language does not create culture. Language is used to express and assist in understanding the phenomenon but communication takes knowing and intended interaction with others and culture does not. It is important that we take a look at the very source of each.
When asking which comes first, we find ourselves asking about prehistoric man. Language can exist in many primitive forms. Body language for example, is often viewed as the most basic form of communication. But what about a genetic code? A mother who takes care of her young, is that language? Is that culture? Can instinct be considered a primitive form of either?
When a person first encounters an interaction with another, he or she is faced with elements that move them towards communication. Primitive situations expose raw emotions, for example desire and fear. That is where culture is hiding. Within that first encounter, the thinking man must appreciate the beauty or the danger within something like a tool. Simply seeing a club to make the one male look imposing to the others is less communication, less language and far more of a social structure and cultural standard. It in fact touches on almost all the definitions and interpretations of the word culture. Prehistoric man had to have an appreciation for the savage art of being, in order to form a structure for social interaction.
Humans knew beauty and likely appreciated the same sunset long before they fought over the better place to watch it from. One family clan finds a perfect place to sit and watch the sun in awe. Another family clan also knows of the spot. This is culture developing before the language. The two clans are faced with each other, and have no language to communicate. Do they fight, or sit together?
A solitary man wanders the wild, hunting and gathering to survive since childhood. Since this man does not encounter others, and has no need for language, is he exempt from culture? Are the bones he painted, and the tools he crafted, and the skins he stretched considered without culture? Do they become cultural once another young man watches him in secret, quietly from the bushes? What if he learns this hermits crafty survival techniques introduces them to his village? Was it not culture before it was communicated? Observation and appreciation have the qualities of culture without language when the primitive man is met with innovation, regardless how he reacts.
Clearly there is no way to be certain exactly how such things evolved. But it is certain that a form of culture needs to be present for a need of language to exist. However, culture does not rely upon language. It is a pattern of emotional and intellectual reaction within every individual. Culture can be observed within the appreciation of the things in existence, which lead to language. Primitive tools and the sunset are only two examples of something a prehistoric person might observe without the influence of language that would certainly ignite the fires of culture within them.
Language is a tool of culture. It is something crafted, created and shaped to bring harmony to that growing sense of culture, within a gathering of primitive peoples. The culture is already within them, they look for a way to make it work once met with social interaction. That is the creation of raw and primitive language. Raw and primitive culture is a part of the mystery of perception itself. Perhaps that is the reason it can be interpreted so many different ways. Once broken down culture is an observational interaction with humanity and artistic appreciation. Language is the personal and intentional interaction of one individuals desire to express internal emotions outward to one or more observers.