why does grammar exist?

Grammar is a human atempt to understand how language works. It is as old as written language itself, or so : when Sumerians, the inventors of writing, began to write something else than lists and account reports, they created grammar. When Sumerian tongue faded away but survived as a culture language which had to be taught, about 2000 BCE, the first grammars and dictionaries proper appeared.

One can only speculate.

Humanity is about 2 million years old, during which time there were many distinct stages of evolution. However, these stages were formed gradually. One can assume that language improvements were formed gradually as well.

The ability to speak complex languages is inherent to the most recent stage of humans, homo sapiens sapiens. So language ability is partly biological. Humans with better language abilities were more effective communicaters and therefore they were naturally selected over less capable individuals over the course of thousands of years.

But it is also cultural. Our current science did not evolve overnight. It was likely the same with languages, where individuals made small contributions to the complexity of language, communication was improved as a result, and improvements were passed down through generations by educating children more and more effectively.

Verbal communication may have existed in its simplest grunty form with australopithicus. From there the biological improvements from homo habilis, homo erectus, neanderthals, and finally humans all provided a breakthrough in language ability. But since auditory language leaves no trace and brain tissue tends to disappear over the course of millennia, there is much disagreement about how much we could speak and when.