Due to complexities in geologic structure, heterogeneity, and insufficient borehole information, shale formation faces challenges in accurately estimating the elastic properties of rock which triggers severe technical challenges in safe drilling and completion. These geomechanical properties could be computed from acoustic logs, however, accurate estimation is critical due to log deficit and a higher recovery expense of inadequate datasets. To fill the gap, this study focuses on predicting the sonic properties of rock using deep neural network (Bi-directional long short-time memory, Bi-LSTM) and random forest (RF) algorithms to estimate and evaluate the geomechanical properties of the potential unconventional formation, Permian Basin, situated in West Texas. A total of three wells were examined using both single-well and cross-well prediction algorithms. Log-derived single-well prediction models include a 75:25 ratio for training and testing the data whereas the cross-well includes two wells for training and the remaining well was used for testing. The selected well input logs include compressional wave slowness, resistivity, gamma-ray, porosity, and bulk density to predict shear wave slowness. The results using RF and Bi-LSTM show a promising prediction of geomechanical properties for Permian Basin wells. RF algorithm performed superior for both single and grouped well prediction. The single-well prediction method using the RF algorithm provided the highest accuracy of 99.90% whereas Bi-LSTM gave 93.60%. The best accuracy for a grouped well prediction was achieved employing Bi-LSTM and RF models, i.e., 96.01% and 93.80%. The average prediction including RF and Bi-LSTM algorithms demonstrated that accuracy for single well and cross well prediction is 96% and 94% respectively with an error below 7%. These outcomes show the astonishing capability of artificial intelligence (AI) models trained to create a realistic prediction to unlock unconventional potential when datasets are inadequate. Given adequate training data, operators could leverage these efficient tools by utilizing them to examine fracture interpretations with reduced cost and time when datasets are incomplete and thus increase the hydrocarbon recovery potential.