  We study quantum geometric contributions to the
Berezinskii-Kosterlitz-Thouless (BKT) transition temperature,
$T_{\mathrm{BKT}}$, in the presence of fluctuations beyond BCS theory. Because
quantum geometric effects become progressively more important with stronger
pairing attraction, a full understanding of 2D multi-orbital superconductivity
requires the incorporation of preformed pairs. We find it is through the
effective mass of these pairs that quantum geometry enters the theory and this
suggests that the quantum geometric effects are present in the
non-superconducting pseudogap phase as well. Increasing these geometric
contributions tends to raise $T_{\mathrm{BKT}}$ which then competes with
fluctuation effects that generally depress it. We argue that a way to
physically quantify the magnitude of these geometric terms is in terms of the
ratio of the pairing onset temperature $T^*$ to $T_{\mathrm{BKT}}$. Our paper
calls attention to an experimental study demonstrating how both temperatures
and, thus, their ratio may be currently accessible. They can be extracted from
the same voltage-current measurements which are generally used to establish BKT
physics. We use these observations to provide rough preliminary estimates of
the magnitude of the geometric contributions in, for example, magic angle
twisted bilayer graphene.
