  Ancient, very metal-poor stars offer a window into the earliest epochs of
galaxy formation and assembly. We combine data from the H3 Spectroscopic Survey
and Gaia to measure metallicities, abundances of $\alpha$ elements, stellar
ages, and orbital properties of a sample of 482 very metal-poor (VMP;
[Fe/H]$<-2$) stars in order to constrain their origins. This sample is confined
to $1\lesssim |Z| \lesssim3$ kpc from the Galactic plane. We find that >70% of
VMP stars near the disk are on prograde orbits and this fraction increases
toward lower metallicities. This result unexpected if metal-poor stars are
predominantly accreted from many small systems with no preferred orientation,
as such a scenario would imply a mostly isotropic distribution. Furthermore, we
find there is some evidence for higher fractions of prograde orbits amongst
stars with lower [$\alpha$/Fe]. Isochrone-based ages for main sequence turn-off
stars reveal that these VMP stars are uniformly old ($\approx12$ Gyr)
irrespective of the $\alpha$ abundance and metallicity, suggesting that the
metal-poor population was not born from the same well-mixed gas disk. We
speculate that the VMP population has a heterogeneous origin, including both
in-situ formation in the ancient disk and accretion from a satellite with the
same direction of rotation as the ancient disk at early times. Our precisely
measured ages for these VMP stars on prograde orbits show that the Galaxy has
had a relatively quiescent merging history over most of cosmic time, and
implies the angular momentum alignment of the Galaxy has been in place for at
least 12 Gyr.
