Well, it's complicated. As people like to say, you should try and hire a one-armed attorney, so they won't say, "On the other hand ...."
What most people are thinking of is cases like
Naruto v. Slater, 888 F. 3d 418 (9th Cir. 2018), aka the "monkey selfie case." In that case, the Ninth Circuit (the federal appellate court for the western states) had to determine if Naruto, a seven-year old crested macaque, could bring a copyright claim.
The Court held that "this monkey — and all animals, since they are not human — lacks statutory standing under the Copyright Act. We therefore affirm the judgment of the district court."
Id. at 420.
Cases like this stand for the broad proposition that non-humans would lack the ability to enforce a copyright claim. There is analysis of the language on 425-26.
More recently, in
Thaler v. Perlmutter, Case No. 22-1564 (D.D.C. Aug. 18, 2023), a District Court held that "United States copyright law protects only works of human creation." In doing so, the District Court sided with the copyright office, and against the copyright applicant, who was trying to copyright images created by the AI "Creativity machine."
At this point, I would say that the general consensus is that the answer is no, you cannot copyright things created without human authorship. Of course, there are three important things to remember-
1. There is no bright-line test about how much human involvement is needed. A human artist can use "AI tools" and create an image and copyright it. So the only real dividing line right now is that you can't just have the AI be the author of the work.
2. This is (to date) a statutory issue based upon how the law is written; it's always possible to change the law. (Maybe- it's also possible for courts to reinterpret the Constitution's grant within Art. I).
3. As we all know, settled law can always become ... unsettled.
Nevertheless, the issues with copyright are why large firms that depend on copyright are, to date, avoiding going "full AI." For example, it is well-known that a lot of Hollywood players are hesitant to use "too much AI" not just because of the hypocrisy (they might want to go after the AI companies) but also because they fear adverse court decisions might weaken their copyright claims in the future if (for example) they create shows wholly based on AI scripts.
(Please note that I am providing a very brief overview of a complicated situation; and, as always, you get what you pay for!)