While 3D Gaussian Splatting (3DGS) enables real-time rendering, its training demands workstation-level compute and memory, making mobile deployment impractical under minute-scale time budgets and limited peak memory. We present PocketGS, a mobile scene modeling paradigm that enables on-device 3DGS training under these tightly coupled constraints while preserving high-fidelity reconstruction. PocketGS resolves the fundamental tension between training efficiency, memory compactness, and modeling quality through three co-designed operators: $\mathcal{G}$ builds geometry-faithful point-cloud priors; $\mathcal{I}$ injects local surface statistics to seed anisotropic Gaussians, thereby reducing early conditioning gaps; and $\mathcal{T}$ unrolls alpha compositing with cached intermediates and index-mapped gradient scattering for stable mobile backpropagation. Extensive experiments demonstrate that PocketGS outperforms the powerful mainstream workstation 3DGS baseline under mobile budgets, delivering high-quality reconstructions and enabling a fully on-device, practical capture-to-rendering workflow.