Can your civilian job fire you after putting in notice of joining the military?

Yes they can. It is sad to say that but the employer is allowed to do this. The laws on the book only apply to those currently serving in the National Guard and the Reserves who have to leave their civilian job in order to fulfill their service requirements. Since you are still a civilian waiting to enter the service, those laws do not apply.

I am a dept manager for a company. As a veteran, I'm likely to keep someone around that told me they were going into the military. I'd wait until the last moment to hire a replacement.
My boss, he'd tell me to start the hiring process right away, and if the right guy shows up tomorrow, then I'd be forced to fire you then.
There are no laws that protect your job as a recruit.
Sucks, but that's just the way it is.

California law prohibits public and private employers from discharging or otherwise discriminating against an employee because he or she is a member of the state or U.S. military or is ordered to duty or training (CA Mil. and Vet. Code Sec. 394, Sec. 395).
Effective January 1, 2018, this prohibition against discrimination extends to all terms, conditions, and privileges of employment.
There are a number of laws providing military leave rights and benefits to California's private employees, including:
Leave for training. Employers must grant up to 17 days of temporary, unpaid leave per year to employees in the U.S. reserves, National Guard, or naval militia who are called to engage in drills, training, encampment, naval cruises, special exercises, or like activities. The 17-day period includes time required to travel to and from duty (CA Mil. and Vet. Code Sec. 394.5).
Private employers must grant up to 15 calendar days of unpaid temporary leave to employees in the state military reserve for training, drills, and other inactive duty training (CA Mil. and Vet. Code Sec. 395.9).
Benefits. Private employers may not restrict or terminate any collateral benefit for an employee who is ordered to duty or training for less than 52 weeks (CA Mil. and Vet. Code Sec. 394).
“Collateral benefits” include health care, which may be continued at the employee's expense, life insurance, disability insurance, and seniority status. An employer that restricts benefits in violation of the law is guilty of a misdemeanor and will be liable for actual damages and reasonable attorney's fees incurred by the employee.

The above is intended to protect National Guard and Reserve.

You are not technically covered under military leave acts because you are not officially part of the military yet.

Have you applied for unemployment?