4D Gaussian Splatting (4DGS) enables high-quality dynamic novel view synthesis, yet current models remain monolithic bitstreams that clients must download in full before any frame can be rendered, causing black-screen waits of tens to hundreds of seconds on mobile bandwidth and leaving 4DGS incompatible with modern adaptive-bitrate delivery. Progressive 3DGS compression alleviates this for static scenes, but it acts only on spatial anchors and cannot partition the temporal deformation networks that dominate dynamic-scene size. We present PD-4DGS, the first framework for progressive compression and on-demand transmission of 4DGS. Hierarchical Deformation Decomposition (HDD) externalises the coarse-to-fine motion hierarchy already latent in 4DGS into three independently transmittable layers -- a static scaffold, a global deformation, and a local refinement -- so that any prefix of the bitstream is already renderable, turning a single training run into a scalable, DASH/HLS-compatible bitstream. A Gaussian-entropy attribute rate-distortion loss together with a temporal mask consistency regulariser shrink the base layer while suppressing low-bitrate flicker; a capacity-weighted rollout schedule, gated online by a learnt activation rate rho, then prevents deformation-network under-training without any per-scene hyperparameter. On the Dycheck iPhone benchmark, PD-4DGS cuts the streamed bitstream by >60% at matched rendering fidelity and reduces first-frame latency from 73--930 s to ~1.7 s on a 2 Mbps link, uniquely enabling true on-demand progressive streaming for 4DGS.