Climate change and the COVID-19 pandemic have disrupted the food supply chain across the globe and adversely affected food security. Early estimation of staple crops can assist relevant government agencies to take timely actions for ensuring food security. Reliable crop type maps can play an essential role in monitoring crops, estimating yields, and maintaining smooth food supplies. However, these maps are not available for developing countries until crops have matured and are about to be harvested. The use of remote sensing for accurate crop-type mapping in the first few weeks of sowing remains challenging. Smallholder farming systems and diverse crop types further complicate the challenge. For this study, a ground-based survey is carried out to map fields by recording the coordinates and planted crops in respective fields. The time-series images of the mapped fields are acquired from the Sentinel-2 satellite. A deep learning-based long short-term memory network is used for the accurate mapping of crops at an early growth stage. Results show that staple crops, including rice, wheat, and sugarcane, are classified with 93.77% accuracy as early as the first four weeks of sowing. The proposed method can be applied on a large scale to effectively map crop types for smallholder farms at an early stage, allowing the authorities to plan a seamless availability of food.