PHANGS-JWST First Results: Dust embedded star clusters in NGC 7496 selected via 3.3 $\mu$m PAH emission

The earliest stages of star formation occur enshrouded in dust and are not observable in the optical. Here we leverage the extraordinary new high-resolution infrared imaging from JWST to begin the study of dust-embedded star clusters in nearby galaxies throughout the local volume. We present a technique for identifying dust-embedded clusters in NGC 7496 (18.7 Mpc), the first galaxy to be observed by the PHANGS-JWST Cycle 1 Treasury Survey. We select sources that have strong 3.3$\mu$m PAH emission based on a $\rm F300M-F335M$ color excess, and identify 67 candidate embedded clusters. Only eight of these are found in the PHANGS-HST optically-selected cluster catalog and all are young (six have SED-fit ages of $\sim1$ Myr). We find that this sample of embedded cluster candidates may significantly increase the census of young clusters in NGC 7496 from the PHANGS-HST catalog -- the number of clusters younger than $\sim$2 Myr could be increased by a factor of two. Candidates are preferentially located in dust lanes, and are coincident with peaks in PHANGS-ALMA CO (2-1) maps. We take a first look at concentration indices, luminosity functions, SEDs spanning from 2700A to 21$\mu$m, and stellar masses (estimated to be between $\sim10^4-10^5 M_{\odot}$). The methods tested here provide a basis for future work to derive accurate constraints on the physical properties of embedded clusters, characterize the completeness of cluster samples, and expand analysis to all 19 galaxies in the PHANGS-JWST sample, which will enable basic unsolved problems in star formation and cluster evolution to be addressed.