  Close-in gas giants present a surprising range of stellar obliquity, the
angle between a planet's orbital axis and its host star's spin axis. It is
unclear whether the obliquities reflect the planets' dynamical history (e.g.,
aligned for in situ formation or disk migration versus misaligned for
high-eccentricity tidal migration) or whether other mechanisms (e.g.,
primordial misalignment or planet-star interactions) are more important in
sculpting the obliquity distribution. Here we present the stellar obliquity
measurement of TOI-1268 (TIC-142394656, $V_{\rm mag} {\sim} 10.9$), a young
K-type dwarf hosting an 8.2-day period, Saturn-sized planet. TOI-1268's lithium
abundance and rotation period suggest the system age between the ages of
Pleiades cluster (${\sim}120$ Myr) and Praesepe cluster (${\sim}670$ Myr).
Using the newly commissioned NEID spectrograph, we constrain the stellar
obliquity of TOI-1268 via the Rossiter-McLaughlin (RM) effect from both radial
velocity (RV) and Doppler Tomography (DT) signals. The 3$\sigma$ upper bounds
of the projected stellar obliquity $|\lambda|$ from both models are below
60$^\circ$. The large host star separation ($a/R_\star {\sim} 17$), combined
with the system's young age, makes it unlikely that the planet has realigned
its host star. The stellar obliquity measurement of TOI-1268 probes the
architecture of a young gas giant beyond the reach of tidal realignment
($a/R_\star {\gtrsim} 10$) and reveals an aligned or slightly misaligned
system.
