  Extremely metal-poor star-forming galaxies (XMPs) represent one of our only
laboratories for study of the low-metallicity stars we expect to encounter at
early epochs. But as our understanding of the $z>6$ universe has improved, it
has become clear that the majority of known XMPs within 100 Mpc host
significantly less prominent massive star populations than their
reionization-era counterparts, severely limiting their utility as testbeds for
interpreting spectral features found at the highest redshifts. Here we present
a new photometric selection technique designed to identify nearby XMPs
dominated by young stellar populations comparable to those expected in the
reionization era. We apply our technique to uncover candidate XMPs in SDSS
imaging at magnitudes $16<i'<23$, extending significantly below the
completeness limits of the SDSS spectroscopic survey. Spectroscopic
observations with the MMT confirm that 32 of the 53 uniformly metal-poor and
high specific star formation rate targets we observed have gas-phase oxygen
abundances $12+\log\mathrm{O/H}<7.7$ ($Z/Z_\odot<0.1$), including two in the
range of the lowest-metallicity galaxies known, $Z/Z_\odot<0.05$. Our
observations shed new light onto the longstanding mystery of He II emission in
star-forming galaxies: we find that the equivalent width of the He II $\lambda
4686$ high-ionization emission line does not scale with that of H$\beta$ in our
sample, suggesting that binary evolution or other processes on $>10$ Myr
timescales contribute substantially to the $\mathrm{He^+}$-ionizing photon
budget in this metallicity regime. Applying such selection techniques coupled
with deep spectroscopy to next-generation photometric surveys like LSST may
eventually provide a basis for an empirical understanding of metal-poor massive
stars.
