To efficiently support large-scale NNs, multi-level hardware, leveraging advanced integration and interconnection technologies, has emerged as a promising solution to counter the slowdown of Moore's law. However, the vast design space of such hardware, coupled with the complexity of their spatial hierarchies and organizations, introduces significant challenges for design space exploration (DSE). Existing DSE tools, which rely on predefined hardware templates to explore parameters for specific architectures, fall short in exploring diverse organizations, spatial hierarchies, and architectural polymorphisms inherent in multi-level hardware. To address these limitations, we present Multi-Level Design Space Exploror (MLDSE), a novel infrastructure for domain-specific DSE of multi-level hardware. MLDSE introduces three key innovations from three basic perspectives of DSE: 1) Modeling: MLDSE introduces a hardware intermediate representation (IR) that can recursively model diverse multi-level hardware with composable elements at various granularities. 2) Mapping: MLDSE provides a comprehensive spatiotemporal mapping IR and mapping primitives, facilitating the mapping strategy exploration on multi-level hardware, especially synchronization and cross-level communication; 3) Simulation: MLDSE supports universal simulator generation based on task-level event-driven simulation mechanism. It features a hardware-consistent scheduling algorithm that can handle general task-level resource contention. Through experiments on LLM workloads, we demonstrate MLDSE's unique capability to perform three-tier DSE spanning architecture, hardware parameter, and mapping.