  We measured the full complex ac conductance of two-dimensional granular
In/InO$_x$ composites using the mutual inductance technique to explore the
transition from a "failed-superconductor-turned anomalous metal" to a robust
superconductor. In this system, room-temperature annealing was adopted to tune
the InO$_x$-mediated coupling between In grains, allowing for the observation
of both a "true" superconductor-to-insulator transition and the emergence of an
intervening anomalous metallic state. In this paper, we show that further
annealing increases the inter-grain coupling, which eliminates the anomalous
metallic phase, but at the same time prevent the emergence of strong
Bose-dominated insulating phase. The complex ac conductance revealed a $T\to0$
saturating dissipative response in a finite magnetic field, coexisting with a
robust superfluid density. The anomalous power-law spectra for the dissipative
response appear to indicate quantum critical behavior proximate to a quantum
superconductor to anomalous-metal transition as probed in the kilo-Hertz range,
and point to signatures of gapless superconductivity in our granular
superconducting system.
