We present an interstellar medium and stellar population analysis of three spectroscopically confirmed z > 7 galaxies in the Early Release Observations JWST/NIRCam and JWST/NIRSpec data of the SMACS J0723.3−7327 cluster. We use the Bayesian spectral energy distribution-fitting code PROSPECTOR with a flexible star formation history (SFH), a variable dust attenuation law, and a self-consistent model of nebular emission (continuum and emission lines). Importantly, we self-consistently fit both the emission line fluxes from JWST/NIRSpec and the broad-band photometry from JWST/NIRCam, taking into account slit-loss effects. We find that these three z=7.6–8.5 galaxies (M⋆ ≈ 108 M⊙) are young with rising SFHs and mass-weighted ages of 3–4 Myr, though we find indications for underlying older stellar populations. The inferred gas-phase metallicities broadly agree with the direct metallicity estimates from the auroral lines. The galaxy with the lowest gas-phase metallicity (Zgas= 0.06 Z⊙) has a steeply rising SFH, is very compact (<0.2 kpc), and has a high star formation rate surface density (ΣSFR ≈ 22 M⊙ yr−1 kpc−2), consistent with rapid gas accretion. The two other objects with higher gas-phase metallicities show more complex multicomponent morphologies on kpc scales, indicating that their recent increase in star formation rate is driven by mergers or internal, gravitational instabilities. We discuss effects of assuming different SFH priors or only fitting the photometric data. Our analysis highlights the strength and importance of combining JWST imaging and spectroscopy for fully assessing the nature of galaxies at the earliest epochs.