The standard $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) cosmological model faces increasing tensions between key observations, motivating tests that probe its underlying assumptions. In a companion Letter [S. M. Koksbang and A. Heinesen, Diagnostic consistency tests of the concordance cosmology, Phys. Rev. Lett. 137, 091001 (2026)], we present a model-independent framework that combines derivatives of the angular diameter distance, $d_A(z)$, and the line-of-sight expansion rate, $\mathcal{H}(z)$, to clarify the physical content of Friedmann-LeMaître-Robertson-Walker (FLRW) consistency relations and to construct a general-spacetime estimator of the cosmic density field. Here, we apply these tests to data, introducing a nonparametric reconstruction method based on symbolic regression combined with bootstrapping to provide data-driven uncertainty estimates. Using supernova and baryon acoustic oscillations data, we reconstruct $d_A$, $\mathcal{H}$, and their derivatives, enabling model-independent evaluation of FLRW relations and recovery of the sky-averaged density field over $z\in [0.38,\sim 2]$. Current data are too sparse to tightly constrain $\mathcal{H}(z)$, and the reconstructed density is consistent with both Planck and Supernova, $H_0$, for the Equation of State (SH0ES) data $\mathrm{\Lambda }\mathrm{CDM}$. Reconstructed FLRW consistency tests show mild to moderate deviations from FLRW expectations at the $\sim 2–4\sigma$ level, although their significance depends on data selection and reconstruction stability. If these indicated deviations from an FLRW geometry are real, it would signify that most of the cosmological solutions considered for solving the cosmological tensions (evolving/interacting dark energy, new types of matter/energy, modified gravity, etc., within the FLRW framework) are ruled out. These preliminary indications highlight the importance of future, denser distance and expansion rate measurements, as well as further work toward standardizing uncertainty estimation for symbolic-regression reconstructions.

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• Cosmological parameters
• Cosmology
• Relativistic aspects of cosmology