  The tension between the diverging density profiles in Lambda Cold Dark Matter
($\Lambda$CDM) simulations and the constant-density inner regions of observed
galaxies is a long-standing challenge known as the `core-cusp' problem. We
demonstrate that the \texttt{SMUGGLE} galaxy formation model implemented in the
\textsc{Arepo} moving mesh code forms constant-density cores in idealized dwarf
galaxies of $M_\star \approx 8 \times 10^7$ M$_{\odot}$ with initially cuspy
dark matter halos of $M_{200} \approx 10^{10}$ M$_{\odot}$. Identical initial
conditions run with the Springel and Hernquist (2003; SH03) feedback model
preserve cuspiness. Literature on the subject has pointed to the low density
threshold for star formation, $\rho_\text{th}$, in SH03-like models as an
obstacle to baryon-induced core formation. Using a \texttt{SMUGGLE} run with
equal $\rho_\text{th}$ to SH03, we demonstrate that core formation can proceed
at low density thresholds, indicating that $\rho_\text{th}$ is insufficient on
its own to determine whether a galaxy develops a core. We suggest that the
ability to resolve a multiphase interstellar medium at sufficiently high
densities is a more reliable indicator of core formation than any individual
model parameter. In \texttt{SMUGGLE}, core formation is accompanied by large
degrees of non-circular motion, with gas rotational velocity profiles that
consistently fall below the circular velocity $v_\text{circ} = \sqrt{GM/R}$ out
to $\sim 2$ kpc. This may artificially mimic larger core sizes when derived
from observable quantities compared to the size measured from the dark matter
distribution ($\sim 0.5$ kpc), highlighting the need for careful modeling in
the inner regions of dwarfs to infer the true distribution of dark matter.
