Tropical Cyclone (TC) genesis forecasting is an important aspect of early warning systems, as it allows the adoption of early warnings and mitigation plans. However, existing methods often rely on binary classification or fail to capture the complex spatio-temporal dependencies that govern TC formation. To address this limitation, this study introduces STAG-Net, a novel Spatio-Temporal Attention-Gated Network designed to directly predict the geographical coordinates of TC genesis. The model uses multivariate variables of meteorological factors such as u-wind, v-wind, relative humidity, temperature, and large-scale dynamic features using a Convolutional Neural Network (CNN), Gated Recurrent Units (GRUs), and a channel-wise attention mechanism in identifying both spatial and temporal characteristics. The methodology takes the initial tropical disturbance data as an input and obtains spatial features in the ERA5 reanalysis dataset that covers 37 isobaric pressure levels. The study also investigates the effect of grid resolution on prediction performance, as four grid sizes were compared, namely $10\times 10$, $20\times 20$, $30\times 30$, and $40\times 40$. The experimental results demonstrate that STAG-Net significantly outperforms existing baselines such as the Dynamic Spatio-temporal model (DST), Spatial Attention Fusing Network (Saf-Net), and a temporal-only model. Notably, the model achieves an average MAE of ${2.67}^{\circ }$, MSE of 13.24, RMSE of 3.45, and $R^2$ of 0.87045, corresponding to performance improvements of 9.75%, 26.25%, 12.92%, and 4.27%, respectively, over the baseline model. The results also indicate that the $30\times 30$ grid configuration was found to be the most effective. The results highlight the significance of the proposed approach for the TC genesis location prediction task.