Abstract Recent discussions about supernova magnitude evolution have raised doubts about the robustness of the late-universe acceleration. In a previous letter, Huang did a null test of the cosmic acceleration by using a Parameterization based on the cosmic Age (PAge), which covers a broad class of cosmological models including the standard Λ cold dark matter model and its many extensions. In this work, we continue to explore the cosmic expansion history with the PAge approximation. Using baryon acoustic oscillations (without a CMB prior on the acoustic scale), gravitational strong lens time delay, and passively evolving early galaxies as cosmic chronometers, we obtain ≳ 4σ detections of cosmic acceleration for both flat and nonflat PAge universes. In the nonflat case, we find a novel ≳3σ tension between the spatial curvatures derived from baryon acoustic oscillations and strong lens time delay. Implications and possible systematics are discussed.