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We carry out a blind search of 3 mm continuum sources using the ALMA Science Archive to derive the first galaxy number counts at this wavelength. The analyzed data are drawn from observations toward three extragalactic legacy fields: COSMOS, CDF-S, and the UDS comprising more than 130 individual ALMA Band 3 pointings and an effective survey area of ≈200 arcmin 2 with a continuum sensitivity that allows for the direct detection of unlensed Dusty Star-forming Galaxies (DSFGs) dust emission beyond the epoch of reionization. We present a catalog of 16 sources detected at >5σ with flux densities S 3 ≈ 60-600 μJy from which number counts are derived. These number counts are then used to place constraints on the volume density of DSFGs with an empirical backward evolution model. Our measured 3 mm number counts indicate that the contribution of DSFGs to the cosmic star formation rate density at z ≳ 4 is non-negligible. This is contrary to the generally adopted assumption of a sharply decreasing contribution of obscured galaxies at z > 4 as inferred by optical and near-infrared surveys. This work demonstrates the power of ALMA-3 mm observations, which can reach outstanding continuum sensitivities during typical spectral line science programs. Further constraints on 3 mm selected galaxies will be essential to refine models of galaxy formation and evolution as well as models of early universe dust production mechanisms.