Weird International Applicant !!??

I don’t know about all UCs, but UC Berkeley will consider you as a domestic applicant for admissions purposes. They will not hold it against you for requesting financial aid at the admissions process.
If you get your Greed Card before enrolling, then they may offer you some aid, but this is only left over aid after its been allocated to in-state students, and if you receive your Green Card in Summer/August period, then all the remaining aid may be handed off to other OOS applicants.