How quickly can I get an ID that will allow me to fly within the US?

I would suggest that you go to the DMV tomorrow and apply for a non-driver ID. The card will be mailed to you, and it might come in the next two weeks if you are lucky.

In principle you could also apply for a driver's license, but this will also require you to take some tests, and adds the risk that you might not pass. If you would have to take a road test, this might require an appointment which may not be available right away.

A passport renewal will probably take more than two weeks. Expedited processing might make it happen in time, but is quite expensive. There can be a possibility for same-day passport renewal if you go to a passport agency, but there are only three in California, and this also typically requires proof of imminent international travel.

Even if you don't get your ID in time, you can still go to the airport and hope that TSA can verify your identity. See https://www.tsa.gov/travel/security-screening/identification under "Forget Your ID?". Bring every form of identification you have (the expired passport, student ID, credit card, utility bills, library card, receipt from your driver's license application, etc.).

You don't necessarily need a state ID. TSA will accept alternate ID.

A driver's license is simply a state ID card that also authorizes driving.

Your best hope is to get a California state ID card. I recommend you do not overload the task and try to get your driver's license also, because that's a huge production. However you can ask whether a REAL ID card can happen as fast as a plain ID, if so, it's a few dollars now but will save you the trouble of returning next year when it will be a total madhouse because REAL ID will be required to fly after October 2020.

California is being forced into REAL ID by TSA, so they have tightened up on the documents you require for plain IDs also. You need several types of documents:

• an original birth certificate, passport or similar
• social security number, or for REAL ID, an original social security card or documents that show your social securiry number, such as a paystub.
• proof of residency: certain items of mail, mailed to you at a particular address in the state that is not a PO box or PMB. If you don't have this yet, you're in trouble :b

If you already have all the documents required on the DMV website, just go tomorrow morning to a DMV an hour before they open and get in line. Figure on a good long while there. Some have a system where your first stop is a clerk who checks to see that you have all the required paperwork, and then you "take a number", and may let you run home and get the missing piece while you are in the queue. So don't let your ride leave you there until you know you have everything.

The Federal SSA office wasn't bad to deal with (they're all over). They do not like expired documents, so if you don't have a Social Security card, get it before your passport expires.

Oh, and one more thing. Chances are the SSA office is closed due to the Federal shutdown.