This study optimized the input processing factors, namely compression force, pressing speed, heating temperature, and heating time, for extracting oil from desiccated coconut medium using a vertical compression process by applying a maximum load of 100 kN. The samples’ pressing height of 100 mm was measured using a vessel chamber of diameter 60 mm with a plunger. The Box–Behnken design was used to generate the factors’ combinations of 27 experimental runs with each input factor set at three levels. The response surface regression technique was used to determine the optimum input factors of the calculated responses: oil yield (%), oil expression efficiency (%), and energy (J). The optimum factors’ levels were the compression force 65 kN, pressing speed 5 mm min−1, heating temperature 80 °C, and heating time 52.5 min. The predicted values of the responses were 48.48%, 78.35%, and 749.58 J. These values were validated based on additional experiments producing 48.18 ± 0.45%, 77.86 ± 0.72%, and 731.36 ± 8.04 J. The percentage error values between the experimental and the predicted values ranged from 0.82 ± 0.65 to 2.43 ± 1.07%, confirming the suitability of the established regression models for estimating the responses.