Writing is a human invention. We have plenty of evidence of its invention and of its improvement down the ages. It would make no sense to assume that writing somehow 'just appeared'. A magical origin of writing would presuppose that our brains are hard wired to read, but we all know that reading and writing are skills that must be taught in a formal manner. Again, if we were 'hard wired' for written language then we would all use a single writing method, regardless of language. Writing is most definitely invented.
Spoken language is an entirely different matter. It evolved. That is to say, first humans evolved language, and then language itself evolved somewhat independently. Our primitive ancestors no doubt found that sticks and stones make useful tools, but they must have found language to be the most powerful and universal of all tools.
Whatever the field of human intellectual endeavour, language is the key to all understanding. Only in the fields of painting and sculpture, games and sports can we achieve much without language. In all other areas proficiency in language confers a massive advantage. Language is the tool that gave humans potential mastery of their environment.
Despite many attempts to invent better, more universal languages, these inventions never live up to expectations, never enjoy wide adoption. The task is too great - human language is the only truly universal tool - hence it must be capable of describing everything in the universe and every interaction of things in the universe, everything which is known, everything which might come to be known and everything which a human can imagine. No one person or group has the skill or knowledge to build such a powerful tool from scratch.
The evolutionary advantage of early language.
Imagine a primitive group of hunter-gatherers. A social structure requires a command structure, a 'pecking order'. Without language, there is only one way to command somebody to, let us say, pick fruit, and that is to demonstrate by physical action. On later occasions gestures may be enough. But if there are many fruits in the same area there is only one way to show which fruits are required - physical demonstration.
The great advantage of language for the group is a fuller division of labour. Whether instructed by gesture or by voice, if one person or group can be sent unsupervised to perform a task then the supervisor is free to be productive. Language has survival value because it increases the productivity of the group through planning, command and control. even older and feebler members of the group can now contribute, through instruction and education.
Spoken language may have evolved at first in parallel with gestural language. It is not widely appreciated just how much of human language is keyed, not to the visual but to the haptic senses. We commonly talk about having a grasp of or a feel for an idea. It appears that we solve some physical problems by imagining, or even performing, physical movements. We also learn much by simply watching others at work - human see, human do.
Perhaps early language evolved from a labeling of a gesture with a sound. If just one person started using a specific sound habitually with a specific gesture, others may well have copied this mannerism. It is a common observation that close groups adopt common behaviours. Once the sound is familiar to the group the accompanying gesture is redundant - the sound has become a word with an attached meaning.
Modern society without language is impossible to even imagine. Through language we have records of past achievements and can replicate them. The immense social and survival value of parent nurturing is extended back into the past as far as tribe memory and written records can take us. Long dead ancestors continue to contribute in a meaningful way to our children's welfare.
Psychologically speaking, we are possibly more a product of our society than of our genes. But our society is based on language, controlled through language. In a sense, society is language. We are born into a world dominated by language. We acquire language as children, and then we are educated through language. We use language to interact with society at all levels. It is only through language that we get to keep the specialist knowledge of many long dead ancestors.
Language is the glue that binds us together. We would not be what we are today without language. In a time long gone, in a place unknown, a group of not quite humans huddled together in a cave, fearful of the noise of rain, thunder and howling wind outside. By some as yet unknown process they had progressed beyond the grunts and gestures of a purely command-oriented language. For them, there was a comfort and a joy in the feel of language, in its flowing rhythms and its power. Perhaps they had learned to chant rhythms together. Language, a gift from evolution, became something more than a tool. One day it would blossom into poetry and song. But in a stone-age cave it would have been, for our ancestors, the greatest force for bonding a collection of genetically related beings into a true community. In a fire-lit shelter against a bewildering maelstrom of natural forces, language was surely the brightest candle against the raging darkness.