It is uncertain whether or not low-mass Population III stars ever existed. While limits on the number density of Population III stars with $M_{ast} approx 0.8~M_{odot}$ have been derived using Sloan Digital Sky Survey (SDSS) data, little is known about the occurrence of Population III stars at lower masses. In the absence of reliable parallaxes, the spectra of metal-poor main sequence (MPMS) stars with $M_{ast} lesssim 0.8~M_{odot}$ can easily be confused with cool white dwarfs. To resolve this ambiguity, we present a classifier that differentiates between MPMS stars and white dwarfs based on photometry and/or spectroscopy without the use of parallax information. We build and train our classifier using state-of-the-art theoretical spectra and evaluate it on existing SDSS-based classifications for objects with reliable Gaia DR2 parallaxes. We then apply our classifier to a large catalog of objects with SDSS photometry and spectroscopy to search for MPMS candidates. We discover several previously unknown candidate extremely metal-poor (EMP) stars and recover numerous confirmed EMP stars already in the literature. We conclude that archival SDSS spectroscopy has already been exhaustively searched for EMP stars. We predict that the lowest-mass primordial-composition stars will have redder optical-to-infrared colors than cool white dwarfs at constant effective temperature due to surface gravity-dependent collision-induced absorption from molecular hydrogen. We suggest that the application of our classifier to data produced by next-generation spectroscopic surveys will set stronger constraints on the number density of low-mass Population III stars in the Milky Way.
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