This paper proposes a sequential optimization framework for joint localization of microphones and sound sources based on Time Difference of Arrival (TDOA) observations. Conventional batch optimization methods simultaneously estimate all microphone and source positions, making the optimization highly sensitive to initialization due to the high dimensionality of the search space. In large-scale environments, the optimization process may converge to undesirable local or mirror solutions, resulting in severe estimation errors. To address this issue, the proposed method first selects a small set of reference microphones based on geometric consistency derived from TDOA observations and constructs a stable small-scale estimation core. The estimation target is then progressively expanded using asymptotic approximation and sequential numerical optimization. This sequential initialization strategy allows each optimization stage to start near the global optimum and effectively suppresses estimation failures caused by poor initialization. Numerical simulations were conducted for large-scale joint localization involving 30 microphones and 20 sound sources, and the proposed method was compared with a conventional batch optimization approach. The results demonstrated that the proposed framework maintains comparable median estimation accuracy while significantly suppressing large outliers in the 95th percentile statistics. Furthermore, stable localization performance was achieved under noisy conditions without substantially increasing the computational cost.