hcad apprasial?

I purchased my house for 270k in October this year. The HCAD appraisal for my house for 2023 is 313k, but since the previous owners had a homestead exemption this year, I didn't really have to pay any taxes. Since I purchased in October which will around 3 months from the appraisal date (Jan 1, 2024), do you think HCAD will honor this price and appraise it for 270k since it was so recent, if I decide to protest, if I don't like their apprasial value? A home 2 doors down has sold for $280k as well. Does anyone have any experience with the protests?