Based on triaxial seepage tests, the effect of curing methods on the seepage characteristics of concrete structures is investigated. Subsequently, a framework for structural-level underground concrete seepage analysis is established. Particularly, the influences of the curing method, vertical load, and seepage pressure on concrete permeability are examined. Then, time-dependent seepage models are developed for concrete cured under variable-temperature and standard conditions, considering the load and seepage coupling. Further, random field theory is employed to construct the seepage analytical framework, accounting for the spatial and temporal randomness of design parameters. The proposed analytical framework was applied to a tunnel with high water temperature in southwest China. The findings are as follows. (1) The curing method plays a pivotal role in determining concrete permeability. Variable-temperature curing improves concrete compactness and reduces the permeability coefficient. (2) Under identical curing conditions and low stress levels (within 5 MPa), the permeability coefficient decreases with increasing compressive stress, and this relationship can be approximated by a cubic polynomial. (3) Variable-temperature curing systematically enhances lining impermeability; compared with standard curing, it not only reduces the initial permeability coefficient of linings but also markedly decelerates the degradation of impermeability performance over service time. Under the same service conditions, linings cured under variable-temperature conditions require considerably more time to reach a given deterioration level than those cured under standard conditions, demonstrating that variable-temperature curing effectively refines the concrete microstructure and improves the long-term resistance of linings to seepage erosion.