The SCUBA-2 Ultra Deep Imaging EAO Survey (STUDIES) is a three-year JCMT Large Program aiming to reach the 450 μm confusion limit in the COSMOS-CANDELS region to study a representative sample of the high-redshift far-infrared galaxy population that gives rise to the bulk of the far-infrared background. We present the first-year data from STUDIES. We reached a 450 μm noise level of 0.91 mJy for point sources at the map center, covered an area of 151 arcmin², and detected 98 and 141 sources at 4.0σ and 3.5σ, respectively. Our derived counts are best constrained in the 3.5–25 mJy regime using directly detected sources. Below the detection limits, our fluctuation analysis further constrains the slope of the counts down to 1 mJy. The resulting counts at 1–25 mJy are consistent with a power law having a slope of −2.59 (±0.10 for 3.5–25 mJy, and for 1–3.5 mJy). There is no evidence of a faint-end termination or turnover of the counts in this flux density range. Our counts are also consistent with previous SCUBA-2 blank-field and lensing-cluster surveys. The integrated surface brightness from our counts down to 1 mJy is 90.0 ± 17.2 Jy deg^−2, which can account for up to of the COBE 450 μm background. We show that Herschel counts at 350 and 500 μm are significantly higher than our 450 μm counts, likely caused by its large beam and source clustering. High angular resolution instruments like SCUBA-2 at 450 μm are therefore highly beneficial for measuring the luminosity and spatial density of high-redshift dusty galaxies....