The global energy structure is on a low-carbon transition path featuring more natural gas consumption, and global natural gas demand has been increasing fast. Planning and operation of a natural gas supply system at a transient stage with multiple supply sources, end-consumers, and large infrastructure with multiple sub-systems are challenging tasks. Spatial and seasonal mismatch of natural gas supply and demand makes the natural gas distribution and infrastructure construction planning problem even more complex. Without proper planning, insufficient construction could lead to a shortage of natural gas supply, whilst excessive construction could lead to a higher cost. Quantitative analysis technologies are needed to facilitate decision-making during the transient stage of a natural gas system. In this work, we propose a monthly-scale multi-period and multi-regional modelling and optimization framework for planning and operation of a natural gas supply system at a transient stage, with a case study of the natural gas supply system in China. The optimal planning and operation strategy of the natural gas supply system in China by 2050 is obtained by minimizing the lifespan overall cost. Gaps between actual planning and the optimal planning are pointed out. Finally, policy suggestions are summarized, including establishing market-oriented pricing mechanisms, managing infrastructure centrally, promoting coordination amongst provinces when formulating projections, accelerating current infrastructure construction, and predicting natural gas demand and prices reasonably.