We present the first combined analysis of the statistical rate function \(f\) in superallowed \(\beta\) decays with \textit{ab initio} calculations and data. We focus on \({}^{10}\text{C}\rightarrow {}^{10}\text{B}^*\), \({}^{14}\text{O}\rightarrow {}^{14}\text{N}^*\) and \({}^{26\text{m}}\text{Al}\rightarrow {}^{26}\text{Mg}\), all of which are important channels for the precise determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element \(V_{ud}\). Nuclear charge form factors are obtained by combining experimental data on nuclear charge radii and theory calculations of ratios of moments with the in-medium similarity renormalization group, while the \(\beta\) decay form factors are derived from exact isospin relations. This enables a rigorous study of the nuclear shape dependence in the statistical rate function \(f\) and the quantification of its uncertainties from both experiment and theory. The calculation leads to a more precise test for the first-row CKM unitarity with reduced theoretical uncertainties. This work demonstrates a reliable strategy for combining nuclear many-body calculations with high-precision nuclear data to describe \(\beta\) decays at tree level for precision tests of the Standard Model.