  We study feedback-driven cold dark matter core creation in the EDGE suite of
radiation-hydrodynamical dwarf galaxy simulations. Understanding this process
is crucial when using observed dwarf galaxies to constrain the particle nature
of dark matter. While previous studies have shown the stellar-mass to halo-mass
ratio $(M_{\star} / M_{200})$ determines the extent of core creation, we find
that in low-mass dwarfs there is a crucial additional effect, namely the timing
of star formation relative to reionisation. Sustained post-reionisation star
formation decreases central dark matter density through potential fluctuations;
conversely, pre-reionisation star formation is too short-lived to have such an
effect. In fact, large stellar masses accrued prior to reionisation are a
strong indicator of early collapse, and therefore indicative of an increased
central dark matter density. We parameterise this differentiated effect by
considering $M_{\star,\mathrm{post}}/M_{\star,\mathrm{pre}}$, where the
numerator and denominator represent the amount of star formation after and
before $z\sim6.5$, respectively. Our study covers the halo mass range $10^9 <
M_{200} < 10^{10} M_\odot$ (stellar masses between $10^4 < M_{\star} < 10^8
M_\odot$), spanning both ultra-faint and classical dwarfs. In this regime,
$M_{\star,\mathrm{post}}/M_{\star,\mathrm{pre}}$ correlates almost perfectly
with the central dark matter density at $z=0$, even when including simulations
with a substantially different variant of feedback and cooling. We provide
fitting formulae to describe the newfound dependence.
