Two-dimensional materials with intrinsic superconductivity and nontrivial topology represent a frontier for discovering exotic quantum states and potential applications in quantum devices. Here, we report the first comprehensive theoretical investigation of superconductivity in monolayer and bilayer ${\mathrm{Cu}}_2\mathrm{N}$. The monolayer ${\mathrm{Cu}}_2\mathrm{N}$ has been recently synthesized experimentally and features a unique checkerboard lattice with topological nodal lines. Following this experimental breakthrough, we predict phonon-mediated superconductivity with transition temperatures ($T_c$) of 3.8 K (monolayer) and 7.9 K (bilayer) arising from strong electron-phonon coupling ($\lambda =0.76$ and 0.84, respectively) mediated primarily by Cu $d$-orbitals and low-frequency phonon modes. The bilayer shows 84% $T_c$ enhancement through additional interlayer vibrational modes that strengthen Cu $d$-orbital coupling via enhanced out-of-plane vibrations. Strain engineering enhances monolayer $T_c$ to 4.5 K under 0.2% compressive strain through optimized electronic density of states and phonon softening. We identify a practical synthesis pathway involving multilayer growth followed by controlled exfoliation with moderate energy cost ($0.97{\mathrm{J}/\mathrm{m}}^2$). Our results demonstrate that ${\mathrm{Cu}}_2\mathrm{N}$, featuring coexisting topological nodal lines and phonon-mediated superconductivity, represents a promising experimental platform for investigating potential topological superconducting behavior in accessible two-dimensional systems.

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• Electron-phonon coupling
• First-principles calculations
• Superconductivity
• Electronic structure
• Topological superconductors
• Two-dimensional electron system
• Density functional calculations