The minicavity in the streamer to the southwest of the dynamical center of the Galaxy and the unique, nonthermal radio source Sgr A* appear to be physically connected by a chain of plasma that may be in transit from the latter to the former. Recent observations at radio and infrared wavelengths have provided clear evidence that the cavity has an opening radius of ~1'' ≈ 0.04 pc and radiates with a power Lcav ≈ 6 × 1037 ergs s-1. Here, we model the formation of the cavity as the result of an impact between the streamer gas and the post-bow shock gas collimated by a massive (~106 M☉) black hole coincident with Sgr A*. Multiwavelength observations, including those of He I, Brα, and Brγ line emission in the inner ~0.3 pc region of the Galaxy provide strong evidence for the presence of an ambient Galactic center wind with velocity vw ≈ 500-700 km s-1 and mass-loss rate ~3-4 × 10-3 M☉ yr-1. We show that the Bondi-Hoyle process responsible for the accretion of ~1022 g s-1 by Sgr A* also produces a downstream, focused flow with a radius very similar to that of the minicavity and a mechanical luminosity about 2.5 larger than Lcav. In addition, the size and density of the blobs appear to be consistent with the gas characteristics in this flow.