Only works created by humans can be copyrighted. This was borne out when it was determined that a photo a ... monkey? Ape? One of those, took of itself by accident could not have copyright because a person wasn't involved in the creation of the image.
So far, the same has been ruled for works created by GenAI. See all the artworks out there that people were mad about not being able to get copyrighted.
edit: Also see this article. https://www.wordsbywes.ink/articles/tools/llm-generated-text-still-cant-be-copyrighted/