You can terminate it at any time unless your reasoning was illegal, thus wrongful termination.

Wikipedia says that according to explanation by Supreme Court of California no reasoning is required:

[A]n employer may terminate its employees at will, for any or no reason ... the employer may act peremptorily, arbitrarily, or inconsistently, without providing specific protections such as prior warning, fair procedures, objective evaluation, or preferential reassignment ... The mere existence of an employment relationship affords no expectation, protectable by law, that employment will continue, or will end only on certain conditions, unless the parties have actually adopted such terms.

IANAL But my understanding is "At will employment" does mean the employer can fire you for an illegal reason such as your race or as retaliation for a complaint. It really just means that the employer does not have to give the legal reason at the time of firing and there is no law requiring warning warnings or a formal evaluation system.

It's on the employee to prove that the company fired them illegally. For example, if the employee had an email showing that their boss said "I hate X because he's black" then the employee would probably win.

No reasoning is required, but they did give a reason, so that is mute.