Enhanced superconductivity in two-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Cu</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mi mathvariant="normal">N</mml:mi> </mml:mrow> </mml:math> : First-p

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 ($\ensuremath{\lambda}=0.76$ 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.