The copyright office does not determine the standards for copyright. They are an advisory and notary organization.
Only Congress and the courts do. Copyright exists from the moment a work is created, and does not need to be registered with the copyright office.
The law isn't that complicated; if a work was created with a human being with intent, it's probably eligible for copyright protections.
As long as you can convince a court that you did this, the tools you used are not relevant. The vast majority of LLM art falls in this bucket.
Do you own the copyright to a painting you commissioned or does the artist? You may have described what you wanted, but the creative work is the output of the artist. Same with an LLM.