Recently, the Large Language Model-based Phoneme-to-Grapheme (LLM-P2G) method has shown excellent performance in speech recognition tasks and has become a feasible direction to replace the traditional WFST decoding method. This framework takes into account both recognition accuracy and system scalability through two-stage modeling of phoneme prediction and text generation. However, the existing LLM-P2G adopts the Top-K Marginalized (TKM) training strategy, and its candidate phoneme sequences rely on beam search generation, which has problems such as insufficient path diversity, low training efficiency, and high resource overhead. To this end, this paper proposes a sampling marginalized training strategy (Sampling-K Marginalized, SKM), which replaces beam search with random sampling to generate candidate paths, improving marginalized modeling and training efficiency. Experiments were conducted on Polish and German datasets, and the results showed that SKM further improved the model learning convergence speed and recognition performance while maintaining the complexity of the model. Comparative experiments with a speech recognition method that uses a projector combined with a large language model (SpeechLLM) also show that the SKM-driven LLM-P2G has more advantages in recognition accuracy and structural simplicity. The study verified the practical value and application potential of this method in cross-language speech recognition systems.