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We theoretically report on an investigation of sodium carbide system by means of first-principles calculations based on density functional theory. Herein, the diverse sodium-carbon structures are predicted by taking carbon-rich compositions of NaC2 with a carbon hexagon structure as a starting point. Metallic phases of NaC2 at a pressure of 100 GPa are predicted to be stabilized by biaxial strain, culminating in the strain -induced electronic topological transitions, also known as the Lifshitz transitions. We found that the flat band accommodates localized electrons around the Fermi level, originating from the effect of biaxial strain, which results in low-velocity electrons forming up to at least 20% of Cooper pairs. According to the respective phonon-mediated superconductivity, NaC2 is dynamically stable not only without the influence of biaxial strain but also with that of the biaxial tensile strain, indicating possible enhancement of the critical temperature superconductor (Tc). Furthermore, the estimated Tc reaches 29.5 K, slightly higher than 24.7 K for the case without biaxial strain. These findings suggest that the possibility of superconductivity is promoted by the applied biaxial tensile strain. Our findings pave the way for future investigation of high superconductivity in carbon-based materials and suggest the possibility of metal-carbides being synthesisable and exhibiting quite a high Tc superconductivity.