Broadband impedance matching and zero reflection of acoustic waves at a planar interface between two natural materials is a rare phenomenon, unlike its optical counterpart, frequently observed for polarized light incident at the Brewster angle. In this article, it is shown that, by inserting a metamaterial layer between two acoustic materials with different impedance, it is possible to artificially realize an extremely broadband Brewster-like acoustic intromission angle window, in which energy is totally transmitted from one natural medium to the other. The metamaterial buffer, composed of acoustically hard materials with subwavelength tapered apertures, provides an interesting way to match the impedances of two media in a broadband fashion, different from traditional methods like quarter-wave matching or Fabry-Pérot resonances, inherently narrowband due to their resonant nature. This phenomenon may be interesting for a variety of applications including energy harvesting, acoustic imaging, ultrasonic transducer technology, and noise control.