The words "existence" and "change" are abstract and very general. So you're addressing the metaphysical question of why existing beings change. This question goes back at least to Plato and the presocratics, and to Hinduism and Daoism. Setting aside the polytheistic answers, one old answer is that change is an illusion, and that reality is permanent, simple, and unified.

In any case, there's a question of method here. What's the best way to address such a profound question of why there's something rather than nothing and why beings in general change.

Scientists explain how individual systems change according to natural laws, and how the universe formed at a cosmological level. Religions tell familiar stories to comfort us in our ignorance. Mystics try to experience the ultimate nature of reality directly, with peak states of consciousness. And rationalist philosophers speculate, analyze concepts, and present these analyses as armchair, a priori deductions. Whether reality has to be subject to human logic or to our intuitive conceptual distinctions or cultural preconceptions is another matter.