Recent studies on superconductivity in NbSe$_2$ have demonstrated a large anisotropy in the superconducting critical field when the material is reduced to a single monolayer. Motivated by this recent discovery, we use density functional theory (DFT) calculations to quantitatively address the superconducting properties of bulk and monolayer NbSe$_2$. We demonstrate that NbSe$_2$ is close to a ferromagnetic instability, and analyze our results in the context of experimental measurements of the spin susceptibility in NbSe$_2$. We show how this magnetic instability, which is pronounced in a single monolayer, can enable sizeable singlet-triplet mixing of the superconducting order parameter, contrary to contemporary considerations of the pairing symmetry in monolayer NbSe$_2$, and discuss approaches as to how this degree of mixing can be addressed quantitatively within our DFT framework. Our calculations also enable a quantitative description of the large anisotropy of the superconducting critical field, using DFT calculations of monolayer NbSe$_2$ in the normal state
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