  Ultracold Fermi gases subject to tight transverse confinement offer a highly
controllable setting to study the two-dimensional (2D) BCS to
Berezinskii-Kosterlitz-Thouless superfluid crossover. Achieving the 2D regime
requires confining particles to their transverse ground state which presents
challenges in interacting systems. Here, we establish the conditions for an
interacting Fermi gas to behave kinematically 2D. Transverse excitations are
detected by measuring the transverse expansion rate which displays a sudden
increase when the atom number exceeds a critical value $N_{2D}$ signifying a
density driven departure from 2D kinematics. For weak interactions $N_{2D}$ is
set by the aspect ratio of the trap. Close to a Feshbach resonance, however,
the stronger interactions reduce $N_{2D}$ and excitations appear at lower
density.
