"I'm wondering if it's possible for me to file a joint state return in California"
Yes, if you file your federal return using file status MFJ, then you may also file your California return as MFJ. Note that CA's rule is that you must use Form 540NR if either you or your spouse/RDP were a nonresident or part-year resident in the tax year.
https://www.ftb.ca.gov/forms/2022/2022-540nr-booklet.html
Form 540NR:
https://www.ftb.ca.gov/forms/2022/2022-540nr.pdf
You may also file your CA return using the MFS filing status, but if you do then CA's community property rules would apply to the division of income.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
