Real-time 3D Gaussian splatting (3DGS)-based Simultaneous Localization and Mapping (SLAM) in large-scale real-world environments remains challenging, as existing methods often struggle to jointly achieve low-latency pose estimation, 3D Gaussian reconstruction in step with incoming sensor streams, and long-term global consistency. In this paper, we present a tightly coupled LiDAR-Inertial-Visual (LIV) 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, thereby enabling continuous dense mapping. To improve Gaussian initialization quality and accelerate optimization convergence, we introduce a cascaded strategy that combines feed-forward predictions with voxel-based principal component analysis (voxel-PCA) geometric priors. To enhance global consistency in large scenes, we further perform loop closure directly on the optimized global Gaussian map by estimating loop constraints through Gaussian-based Generalized Iterative Closest Point (GICP) registration, followed by pose-graph optimization. In addition, we collected challenging large-scale looped outdoor SLAM sequences with hardware-synchronized LiDAR-camera-IMU and ground-truth trajectories to support realistic and comprehensive evaluation. Extensive experiments on both public datasets and our dataset demonstrate that the proposed method achieves a strong balance among real-time efficiency, localization accuracy, and rendering quality across diverse and challenging real-world scenes.

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