Extremely metal-poor (EMP) stars ([Fe/H]<=-3.0dex) provide a unique window into understanding the first generation of stars and early chemical enrichment of the universe. EMP stars are exceptionally rare, however, and the relatively small number of confirmed discoveries limits our ability to exploit these near-field probes of the first ~500Myr after the Big Bang. Here, a new method to photometrically estimate [Fe/H] from only broadband photometric colors is presented. I show that the method, which utilizes machine-learning algorithms and a training set of ~170000 stars with spectroscopically measured [Fe/H], produces a typical scatter of ~0.29dex. This performance is similar to what is achievable via low-resolution spectroscopy, and outperforms other photometric techniques, while also being more general. I further show that a slight alteration to the model, wherein synthetic EMP stars are added to the training set, yields the robust identification of EMP candidates. In particular, this synthetic-oversampling method recovers ~20% of the EMP stars in the training set, at a precision of ~0.05. Furthermore, ~65% of the false positives from the model are very metal-poor stars ([Fe/H]<=-2.0dex). The synthetic-oversampling method is biased toward the discovery of warm (~F-type) stars, a consequence of the targeting bias from the Sloan Digital Sky Survey/Sloan Extension for Galactic Understanding survey. This EMP selection method represents a significant improvement over alternative broadband optical selection techniques. The models are applied to >12 million stars, with an expected yield of ~600 new EMP stars, which promises to open new avenues for exploring the early universe.