Deconstruction and Chomsky
So, I refer to grammar in the concrete traditional sense of syntax and morphology, not to an abstract concept which is language itself. Human beings are indeed capable of producing language (speech), but language as an expressive means of communication develops to maturity through usage and experience, from an inarticulate level where words are sporadically blurted out (one word, two words, then maybe three or more tied in a commonly agreed-upon string with a meaning), to becoming more and more articulate and expressive. Grammar is the ability of language to express ideas, to joggle with words and create meaning. The human brain is too underdeveloped at its earliest stages to express thought through articulate speech, and grammar.
You also mentioned that language is born independently of culture. Some linguists claim that language reflects our reality which is grasped through culture (poststructuralists). This is why it is difficult to translate from one language into another - they are culture-based. Other linguists mean that language precedes reality, it comes before culture. The precedence of language over reality was clearly formulated by American linguists in the early 20th century by what is known as the Sapir-Whorf theory.
REALITY, LANGUAGE, TRANSLATION: