  The identification of red, apparently massive galaxies at $z>7$ in early JWST
photometry suggests a strongly accelerated timeline compared to standard models
of galaxy growth. A major uncertainty in the interpretation is whether the red
colors are caused by evolved stellar populations, dust, or other effects such
as emission lines or AGN. Here we show that three of the massive galaxy
candidates at $z=6.7-8.4$ have prominent Balmer breaks in JWST/NIRSpec
spectroscopy from the RUBIES program. The Balmer breaks demonstrate
unambiguously that stellar emission dominates at $\lambda_{\rm rest} =
0.4\,\mu$m, and require formation histories extending hundreds of Myr into the
past in galaxies only 600--800 Myr after the Big Bang. Two of the three
galaxies also show broad Balmer lines, with H$\beta$ FWHM $>2500~{\rm
km\,s^{-1}}$, suggesting that dust-reddened AGN contribute to, or even
dominate, the SEDs of these galaxies at $\lambda_{\rm rest}\gtrsim 0.6\,\mu$m.
All three galaxies have relatively narrow [O III] lines, seemingly ruling out a
high-mass interpretation if the lines arise in dynamically-relaxed, inclined
disks. Yet, the inferred masses also remain highly uncertain. We model the
high-quality spectra using Prospector to decompose the continuum into stellar
and AGN components, and explore limiting cases in stellar/AGN contribution.
This produces a wide range of possible stellar masses, spanning $M_\star \sim
10^9 - 10^{11}\,{\rm M_{\odot}}$. Nevertheless, all fits suggest a very early
and rapid formation, most of which follow with a truncation in star formation.
Potential origins and evolutionary tracks for these objects are discussed, from
the cores of massive galaxies to low-mass galaxies with over-massive black
holes. Intriguingly, we find all of these explanations to be incomplete; deeper
and redder data are needed to understand the physics of these systems.
