We validate the discovery of a 2 Earth radii sub-Neptune-size planet around the nearby high proper motion M2.5-dwarf G 9-40 (EPIC 212048748), using high-precision near-infrared (NIR) radial velocity (RV) observations with the Habitable-zone Planet Finder (HPF), precision diffuser-assisted ground-based photometry with a custom narrow-band photometric filter, and adaptive optics imaging. At a distance of \(d=27.9\mathrm{pc}\), G 9-40b is the second closest transiting planet discovered by K2 to date. The planet's large transit depth (\(\sim\)3500ppm), combined with the proximity and brightness of the host star at NIR wavelengths (J=10, K=9.2) makes G 9-40b one of the most favorable sub-Neptune-sized planet orbiting an M-dwarf for transmission spectroscopy with JWST, ARIEL, and the upcoming Extremely Large Telescopes. The star is relatively inactive with a rotation period of \(\sim\)29 days determined from the K2 photometry. To estimate spectroscopic stellar parameters, we describe our implementation of an empirical spectral matching algorithm using the high-resolution NIR HPF spectra. Using this algorithm, we obtain an effective temperature of \(T_{\mathrm{eff}}=3404\pm73\)K, and metallicity of \(\mathrm{Fe/H}=-0.08\pm0.13\). Our RVs, when coupled with the orbital parameters derived from the transit photometry, exclude planet masses above \(11.7 M_\oplus\) with 99.7% confidence assuming a circular orbit. From its radius, we predict a mass of \(M=5.0^{+3.8}_{-1.9} M_\oplus\) and an RV semi-amplitude of \(K=4.1^{+3.1}_{-1.6}\mathrm{m\:s^{-1}}\), making its mass measurable with current RV facilities. We urge further RV follow-up observations to precisely measure its mass, to enable precise transmission spectroscopic measurements in the future.