The integration of Low Earth Orbit (LEO) satellite networks with terrestrial 5G and emerging 6G systems is expected to enable ubiquitous, resilient, and high-capacity connectivity. However, developing and evaluating integrated satellite–terrestrial networks under realistic and reproducible conditions remains challenging due to satellite mobility, dynamic topology, Doppler effects, propagation impairments, heterogeneous network segments, and limited access to large-scale physical satellite infrastructure. Supported by the North Dakota NASA EPSCoR Research Seed Grant program, this project is developing an AI-enabled hybrid emulation–simulation testbed for integrated satellite–terrestrial networks. The platform bridges the gap between conventional simulation and real-world experimentation by combining real network applications and protocol implementations with configurable emulation and simulation of satellite and terrestrial communication environments. The architecture incorporates Linux-based network virtualization and programmable networking, with optional satellite-network simulation and software-defined radio integration. Integrated telemetry enables systematic collection of network performance data and development of datasets for AI/ML-assisted network optimization. The testbed will support investigation of critical challenges including Doppler effects, latency, link variability, handovers, adaptive modulation, and intelligent resource management. The resulting platform will provide a flexible and reproducible environment for evaluating AI-enabled networking strategies and will establish a foundation for future research, student training, and collaborative development of next-generation integrated satellite–terrestrial 6G systems.