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 mag ~ 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 the Pleiades cluster (~120 Myr) and the Prasepe cluster (~670 Myr). Using the newly commissioned NEID spectrograph, we constrain the stellar obliquity of TOI-1268 via the Rossiter-McLaughlin effect from both radial velocity and Doppler tomography signals. The 3σ upper bounds of the projected stellar obliquity ∣λ∣ from both models are below 60°. The large host star separation (a/R ⋆ ~ 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 ⋆ ≳ 10) and reveals an aligned or slightly misaligned system.