  Recent works have used a linear birth metallicity gradient to estimate the
evolution of the [Fe/H] profile in the Galactic disk over time, and infer
stellar birth radii (R$_\text{birth}$) from [Fe/H] and age measurements. These
estimates rely on the evolution of [Fe/H] at the Galactic center ([Fe/H](0,
$\tau$)) and the birth metallicity gradient ($\nabla$[Fe/H]($\tau)$) over time
-- quantities that are unknown and inferred under key assumptions. In this
work, we use the sample of Milky Way/Andromeda analogues from the TNG50
simulation to investigate the ability to recover [Fe/H](R, $\tau$) and
R$_\text{birth}$ in a variety of galaxies. Using stellar disk particles, we
test the assumptions required in estimating R$_\text{birth}$, [Fe/H](0,
$\tau$), and $\nabla$[Fe/H]($\tau)$ using recently proposed methods to
understand when they are valid. We show that $\nabla$[Fe/H]($\tau)$ can be
recovered in most galaxies to within 22% from the range in [Fe/H] across age,
with better accuracy for more massive and stronger barred galaxies. We also
find that the true central metallicity is unrepresentative of the genuine disk
[Fe/H] profile; thus we propose to use a projected central metallicity instead.
About half of the galaxies in our sample do not have a continuously enriching
projected central metallicity, with a dilution in [Fe/H] correlating with
mergers. Most importantly, galaxy-specific [Fe/H](R, $\tau$) can be constrained
and confirmed by requiring the R$_\text{birth}$ distributions of mono-age,
solar neighborhood populations to follow inside-out formation. We conclude that
examining trends with R$_\text{birth}$ is valid for the Milky Way disk and
similarly structured galaxies, where we expect R$_\text{birth}$ can be
recovered to within 16% assuming today's measurement uncertainties in TNG50.
