Sean T. Linden, Angela Adamo, Alex Pedrini, Daniela Calzetti, Helena Faustino Vieira, Bruce E. Elmegreen, John S. Gallagher, Kelsey Johnson, Matteo Messa, Kathryn Grasha, Ana Duarte-Cabral, Arjan Bik, Giacomo Bortolini, Matteo Correnti, Drew Lapeer, Thomas S. -Y. Lai, Goran Ostlin, Linda J. Smith, Monica Tosi

With Hubble Space Telescope (HST) and James Webb Space Telescope (JWST) observations of NGC~628 spanning 0.3--7.7\,$μ$m, we fit the spectral energy distributions (SEDs) of over 12,000 optically-selected star clusters, emerging young star clusters (eYSCs), and MIRI-selected sources with \textsc{cigale} to derive their ages, masses, extinctions, and dust properties. We find that near-infrared selected eYSC-I (compact Pa$α$ and 3.3,$μ$m PAH emission) and eYSC-II (compact Pa$α$ and diffuse 3.3,$μ$m PAH emssion) sources peak at $\sim$3--5~Myr, where $\sim 12\%$ of the clusters have an $E(B{-}V)>2$, demonstrating the presence of dust-embedded populations as clusters emerge. Further, the distributions of the fractional polycyclic aromatic hydrocarbon (PAH) abundance ($q_{\mathrm PAH}$) and stellar-to-nebular attenuation ratio ($E(B{-}V)_{\rm \star}/E(B{-}V)_{\rm neb}$) suggest an evolutionary sequence in which sources evolve from eYSC-I to eYSC-II as clusters clear their surrounding dust and gas. The photo-dissociation region (PDR) clearing timescale inferred from the ratio of eYSC-I to optically visible stellar clusters is $\sim$4~Myr. Additionally, we find that star clusters in the spiral arms of NGC 628 are preferentially more massive and more dust-reddened than those in inter-arm regions.~Finally, we find that $\sim$65\% of eYSC-I, $\sim$27\% of eYSC-II, and $\sim$40\% of F335M-selected sources coincide with an F770W peak in our MIRI-selected catalog within 4 pixels, confirming that F770W-bright sources preferentially trace the youngest and dustiest regions. Overall, our results highlight the ability of JWST together with \textsc{cigale} model grids to identify and characterize eYSCs during their short-lived embedded phases, and provide constraints on the feedback mechanisms that govern the emergence of stellar clusters.