Optical access networks have been evolving to meet the explosive growth of data traffic. It is foreseeable that the 100Gb/s/λ and beyond passive optical network (PON) will be required in future optical access networks. Coherent optical communication is a promising solution for the future beyond 100G PON. However, the traditional digital signal processing (DSP) for coherent optical communication is difficult to realize fast convergence due to blind and complex algorithms. In this paper, we design a specific preamble structure and propose a burst-mode DSP to achieve fast convergence for the coherent PON. For verifying the feasibility of the proposed scheme, pointto-multi-point (P2MP) coherent PON is experimentally built up based on digital subcarrier multiplexing (DSCM), which is a kind of frequency division multiple access. When the allocated frequency of the optical network unit is suddenly changed, the DSP should converge fast to ensure a low handoff latency. In P2MP coherent PON, the proposed specific preamble structure and burst-mode DSP jointly implement the fast convergence using a short preamble with only 416 symbols. The experimental results show that the 8-Gbaud/SC×8-SCs 400Gb/s-net-rate coherent PON in burst-mode detection achieves the receiver sensitivity of approximately −27dBm at the 20% soft-decision forward error correction limit and approximately 35.5dB optical power budget with an optical pre-amplifier.