According to California DMV you can use your driver's license in California until you become resident of the state:
If you are a visitor in California over 18 and have a valid driver license from your home state or country, you may drive in this state without getting a California driver license as long as your home state license remains valid.
If you become a California resident, you must get a California driver license within 10 days. Residency is established by voting in a California election, paying resident tuition, filing for a homeowner’s property tax exemption, or any other privilege or benefit not ordinarily extended to nonresidents.
The only problem is that you cannot apply for a driver's license you will need to receive a Social Security Number so until you receive that you won't be able to apply anyway so you will be able to use your Polish driver's license until you're eligible to apply.