Using first-principles calculations combined with the L\"owdin partitioning method, we investigate the layer-resolved topological properties of the Ising superconductor $\mathrm{Nb}{\mathrm{Se}}_{2}$ proximity coupled with a two-dimensional metallic ferromagnet ${\mathrm{Fe}}_{3}\mathrm{Ge}{\mathrm{Te}}_{2}$ (FGT). We first reveal that the top $\mathrm{Nb}{\mathrm{Se}}_{2}$ monolayer develops a nontrivial band topology under the lateral compression caused by the FGT overlayer, while the remaining $\mathrm{Nb}{\mathrm{Se}}_{2}$ layers maintain their band triviality. More significantly, the top $\mathrm{Nb}{\mathrm{Se}}_{2}$ monolayer exhibits distinctly different band topology when the FGT magnetization is switched off or on, characterized by a topological invariant ${Z}_{2}=1$ or Chern number $C=1$, respectively. We further confirm that the Ising pairing nature in the top $\mathrm{Nb}{\mathrm{Se}}_{2}$ monolayer is well preserved in the heterostructure. This study not only provides an appealing candidate system for realizing topological Ising superconductivity, but also presents a generic first-principles based approach for describing topological superconductivity beyond prevailing empirical phenomenological modeling.