To be eligible for in-state CA tuition, you and your family need to live in CA for 366 days prior to the residency determination.
When are your parents moving? You can transfer into a UC or CSU prior to your parents moving, however as pointed out above, you will pay OOS costs until you meet the residency requirement. Also OOS transfer applicants get the lowest priority in the transfer process.
Another option would be to attend a CA Community college which has a proven pathway and then transfer to a UC or CSU which would be less expensive as an OOS student for the 1st year. UC’s and CSU’s only take Junior level transfers with rare exceptions so expect to attend 2 years at a CC.