By your logic, human existence is the point in which things exist. And by that logic, fossils wouldn’t exist. Nor dinosaurs, the earth, or even the beginning of the universe (however you believe it came to be).

I would argue that poetry is more than the mere written word arranged in a rhyming schema. It extends to being anything that sparks creativity of the mind. e.g., The colors of the sunset reflecting off the surface of a pond that ripples from an animal jumping on the water. Surely that existed before humans?

Now I would certainly agree that it took humans to best articulate it by being able to write (or otherwise convey) these moments into more than a fleeting moment in their memory.