Abstract The Embedded Discrete Fracture Model (EDFM) has been widely used to simulate fluid flow and transport in unconventional reservoirs, such as shale-gas and tight oil formations. However, EDFM struggles to capture early-time matrix-fracture interactions when using coarse grids due to the extremely low matrix permeability in these reservoirs. To address this limitation, we propose a model that combines the standard EDFM with the Multiple-INteracting-Continua (MINC) proximity function to enhance the accuracy of matrix-fracture interactions in EDFM while maintaining efficiency. For each matrix cell, the MINC proximity function subdivides individual matrix blocks into connected subregions based on iso-surfaces of the fracture distance. Then the MINC transmissibility values between subregions are derived from estimated interface area and subregion thickness, and then added to the standard EDFM connection list. This allows us to increase resolution for matrix and fracture interactions, describe localized effects near fractures such as gradients of pressures, temperatures, and saturations near the fracture surface and within the matrix itself. The proposed EDFM-MINC model is validated by comparing it to global grid refinement and local grid refinement (LGR) approaches. The validation shows that it captures the sharp increase of production at the early time and is aligned with global grid refinement and local grid refinement approaches. Through simulations of practical scenarios, we explore the accuracy of the method to capture early fluid flow behavior and computational efficiency. Comparative studies with the standard EDFM are presented to show the integration of a MINC decomposition of the matrix cells with standard EDFM significantly enhances accuracy in capturing early-time behaviors. By optimizing the grid resolution through MINC, we also achieve better computational efficiency compared to other grid refinement methods. Overall, the EDFM-MINC model improves our understanding of initial production behavior for unconventional reservoirs and offers valuable insights for optimizing production strategies and improving the history matching process.