Once you apply for your California State ID, you'll need to allow up to 60 days for your ID to arrive in the mail. In the meantime, you'll receive "Positive Identification Verification" paperwork.
This documentation may, or may not be enough proof for your doctor. I wish that I could specifically tell you that it will or will not work, but it's hit and miss.
We've seen doctors who do accept a "Positive Identification Verification", we've seen doctors who accept out of state Id, and we've seen doctors that will take a combination of both your out of state ID and your paperwork.
Either way, you've got a good chance to get your recommendation in the first couple days of your arrival. You'll definitely want to apply for that ID right away though, so that you can obtain your County ID Card as well!
Reference Post: https://www.rollitup.org/medical-marijuana/160649-those-live-non-mmj-states.html#post2078388