We develop a theory of quantum $T=0$ phase transition between metal and superconducting (q-SMT) ground states in a two-dimensional metal with frozen-in spatial fluctuations $\delta\lambda(r)$ of the Cooper attraction constant. We show that if the strength of fluctuations $\delta\lambda(r)$ exceeds some critical value, usual mean-field-like scenario of the q-SMT breaks down due to spontaneous
formation of rare local droplets of superconducting phase. We account for the interaction between these droplets by means of a real-space renormalization group (RG) and find that the RG flow near q-SMT is the dual equivalent of the Kosterlitz-Thouless RG. We find that relevant energy/temperature scale drops exponentially upon approach to the q-SMT point. Close to the quantum critical point, in a broad range of low temperatures fluctuations-induced conductivity $\sigma_{fl}$ is nearly $T$-independent. This behaviour reminds a "strange metal" phase, frequently observed near SMT.