  We present maps of ionized gas (traced by Pa$\alpha$ and Br$\alpha$) and 3.3
$\mu$m Polycyclic Aromatic Hydrocarbon (PAH) emission in the nearby spiral
galaxy NGC 628, derived from new JWST/NIRCam data from the FEAST survey. With
this data, we investigate and calibrate the relation between 3.3 $\mu$m PAH
emission and star formation rate (SFR) in and around emerging young star
clusters (eYSCs) on a scale of ${\sim}40$ pc. We find a tight (correlation
coefficient $\rho$${\sim}$0.9) sub-linear (power-law exponent
$\alpha$${\sim}$0.75) relation between the 3.3 $\mu$m PAH luminosity surface
density and SFR traced by Br$\alpha$ for compact, cospatial (within 0.16$''$ or
${\sim}$7 pc) peaks in Pa$\alpha$, Br$\alpha$, and 3.3 $\mu$m (eYSC-I). The
scatter in the relationship does not correlate well with variations in local
interstellar medium (ISM) metallicity due to a radial metallicity gradient, but
rather is likely due to stochastic sampling of the stellar initial mass
function (IMF) and variations in the PAH heating and age of our sources. The
deviation from a linear relation may be explained by PAH destruction in more
intense ionizing environments, variations in age, and IMF stochasticity at
intermediate to low luminosities. We test our results with various continuum
subtraction techniques using combinations of NIRCam bands and find that they
remain robust with only minor differences in the derived slope and intercept.
An unexpected discrepancy is identified between the relations of hydrogen
recombination lines (Pa$\alpha$ versus Br$\alpha$; H$\alpha$ versus
Br$\alpha$).
