Pemeliza, it appears to me that the key part of Ca renter’s post above is this:
When valuing real property (as described in paragraph (a) as the result of a change in ownership (as defined in Revenue and Taxation Code, Section 60, et seq.) for consideration, it shall be rebuttably presumed that the consideration valued in money, whether paid in money or otherwise, is the full cash value of the property. The presumption shall shift the burden of proving value by a preponderance of the evidence to the party seeking to overcome the presumption.
Assuming that this is the current code that covers this issue, it’s pretty clear that the burden is on the assessors office to prove that the price you paid is NOT the full value of the property. No idea exactly what the process is for you to enforce that. You shouldn’t have to appeal, they should have to prove before they set the assessment. Good luck.