Optimizing the performance of large language models (LLMs) on large-scale AI training and inference systems requires a scalable and expressive mechanism to model distributed workload execution. Such modeling is essential for pre-deployment system-level optimizations (e.g., parallelization strategies) and design-space explorations. While recent efforts have proposed collecting execution traces from real systems, access to large-scale infrastructure remains limited to major cloud providers. Moreover, traces obtained from existing platforms cannot be easily adapted to study future larger-scale system configurations. We introduce Symbolic Tensor grAph GEnerator(STAGE), a framework that synthesizes high-fidelity execution traces to accurately model LLM workloads. STAGE supports a comprehensive set of parallelization strategies, allowing users to systematically explore a wide spectrum of LLM architectures and system configurations. STAGE demonstrates its scalability by synthesizing high-fidelity LLM traces spanning over 32K GPUs, while preserving tensor-level accuracy in compute, memory, and communication. STAGE is publicly available to facilitate further research in distributed machine learning systems: https://github.com/astra-sim/symbolic tensor graph