ALMA observations of the Galactic center with spatial resolution $2.61times0.97$ resulted in the detection of 11 SiO (5-4) clumps of molecular gas within 0.6pc (15$$) of Sgr A*, interior to the 2-pc circumnuclear molecular ring. The three SiO (5-4) clumps closest to Sgr A* show the largest central velocities, $sim150$ kms, and broadest asymmetric linewidths with full width zero intensity (FWZI) $sim110-147$ kms. The remaining clumps, distributed mainly to the NE of the ionized mini-spiral, have narrow FWZI ($sim18-56$ kms). Using CARMA SiO (2-1) data, LVG modeling of the the SiO line ratios for the broad velocity clumps, constrains the column density N(SiO) $sim10^{14}$ cm$^{-2}$, and the H$_2$ gas density n$_{rm H_2}=(3-9)times10^5$ cm$^{-3}$ for an assumed kinetic temperature 100-200K. The SiO clumps are interpreted as highly embedded protostellar outflows, signifying an early stage of massive star formation near Sgr A* in the last $10^4-10^5$ years. Support for this interpretation is provided by the SiO (5-4) line luminosities and velocity widths which lie in the range measured for protostellar outflows in star forming regions in the Galaxy. Furthermore, SED modeling of stellar sources shows two YSO candidates near SiO clumps, supporting in-situ star formation near Sgr A*. We discuss the nature of star formation where the gravitational potential of the black hole dominates. In particular, we suggest that external radiative pressure exerted on self-shielded molecular clouds enhances the gas density, before the gas cloud become gravitationally unstable near Sgr A*. Alternatively, collisions between clumps in the ring may trigger gravitational collapse.
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