Bedsores/Pressure Injuries (PIs) are the second most common diagnosis in healthcare system billing records in the United States and account for 60,000 deaths annually. Hospital-Acquired Pressure Injuries (HAPIs) are one classification of PIs and indicate injuries that occurred while the patient was cared for within the hospital. Until now, all studies have predicted who will develop HAPI using classic machine algorithms, which provides incomplete information for the clinical team. Knowing who will develop HAPI does not help differentiate at which point those predicted patients will develop HAPIs; no studies have investigated when HAPI develops for predicted at-risk patients. This research aims to develop a hybrid system of Random Forest (RF) and Braden Scale to predict HAPI time by considering the changes in patients' diagnoses from admission until HAPI occurrence. Real-time diagnoses and risk factors were collected daily for 485 patients from admission until HAPI occurrence, which resulted in 4619 records. Then for each record, HAPI time was calculated from the day of diagnosis until HAPI occurrence. Recursive Feature Elimination (RFE) selected the best factors among the 60 factors. The dataset was separated into 80% training (10-fold cross-validation) and 20% testing. Grid Search (GS) with RF (GS-RF) was adopted to predict HAPI time using collected risk factors, including Braden Scale. Then, the proposed model was compared with the seven most common algorithms used to predict HAPI; each was replicated for 50 different experiments. GS-RF achieved the best Area Under the Curve (AUC) (91.20 ± 0.26) and Geometric Mean (G-mean) (91.17 ± 0.26) compared to the seven algorithms. RFE selected 43 factors. The most dominant interactable risk factors in predicting HAPI time were visiting ICU during hospitalization, Braden subscales, BMI, Stimuli Anesthesia, patient refusal to change position, and another lab diagnosis. Identifying when the patient is likely to develop HAPI can target early intervention when it is needed most and reduces unnecessary burden on patients and care teams when patients are at lower risk, which further individualizes the plan of care.