Achieving real-time Simultaneous Localization and Mapping (SLAM) based on 3D Gaussian splatting (3DGS) in large-scale real-world environments remains challenging, as existing methods still struggle to jointly achieve low-latency pose estimation, continuous 3D Gaussian reconstruction, and long-term global consistency. In this paper, we present a tightly coupled LiDAR-Inertial-Visual 3DGS-based SLAM framework for real-time pose estimation and photorealistic mapping in large-scale real-world scenes. The system executes state estimation and 3D Gaussian primitive initialization in parallel with global Gaussian optimization, enabling continuous dense mapping. To improve Gaussian initialization quality and accelerate optimization convergence, we introduce a cascaded strategy that combines feed-forward predictions with geometric priors derived from voxel-based principal component analysis. To enhance global consistency, we perform loop closure directly on the optimized global Gaussian map by estimating loop constraints through Gaussian-based Generalized Iterative Closest Point registration, followed by pose-graph optimization. We also collect challenging large-scale looped outdoor sequences with hardware-synchronized LiDAR-camera-IMU and ground-truth trajectories for realistic evaluation. Extensive experiments on both public datasets and our dataset demonstrate that the proposed method achieves a state of the art among real-time efficiency, localization accuracy, and rendering quality across diverse real-world scenes.