Coconut (Cocos nucifera) fruit has attracted consumer interest due to its health benefits, especially the consumption of coconut water produced from 6–7-month-old coconut fruit. Consequently, by-products from young coconut fruit are also being expanded, including coconut mesocarp containing phenolic compounds. Therefore, this study aimed to provide new applications for young coconut mesocarp wastes. Specifically, optimizing the ultrasound-assisted extraction (UAE) of phenolic compounds from coconut mesocarp using a Box–Behnken design in conjunction with response surface methodology (RSM). The effects of three extraction variables, such as temperature (10–70 °C), solvent-to-sample ratio (20:1–10:1 mL g−1), and pulse duty cycle (0.4–1.0 s−1) were examined on the level of total phenolic content (TPC) and antioxidant activity of the extract. Subsequently, the optimum UAE condition was predicted using RSM models with coefficients of determination (R2) higher than 0.94, low prediction errors (less than 2.34), and non-significant lack-of-fit values (p < 0.05) for the two responses. Extraction time was evaluated through kinetic (5 to 25 min) studies applying the optimum extraction temperature (70 °C), solvent-to-sample ratio (20:1 mL g−1), and pulse duty cycle (0.55 s−1). An efficient extraction was achieved within 5 min, resulting in an extract with 47.78 ± 1.24 mg GAE 100 g−1 DW for the total phenolic compounds and high antioxidant activity (87.28 ± 1.01% DPPH). Extraction by ultrasound was then concluded to facilitate a fast extraction rate with high reproducibility (coefficients of variation were less than 3% in the levels of antioxidant activity and phenolic compounds).