A critical challenge in particle physics is combining results from diverse experimental setups that measure the same physical quantity to enhance precision and statistical power, a process known as a global fit. Global fits of sterile neutrino searches, hunts for additional neutrino oscillation frequencies and amplitudes, present an intriguing case study. In such a scenario, the key assumptions underlying Wilks’ theorem, a cornerstone of most classic frequentist analyses, do not hold. The method of Feldman and Cousins, a trials-based approach which does not assume Wilks’ theorem, becomes computationally prohibitive for complex or intractable likelihoods. To bypass this limitation, we borrow a technique from simulation-based inference (SBI) to estimate likelihood ratios for use in building trials-based confidence intervals, speeding up test statistic evaluations by a factor >104 per grid point, resulting in a faster, but approximate, frequentist fitting framework. Applied to a subset of sterile neutrino search data involving the disappearance of muon-flavor (anti)neutrinos, our method leverages machine learning (ML) to compute frequentist confidence intervals while significantly reducing computational expense. In addition, the SBI-based approach holds additional value by recognizing underlying systematic uncertainties that the Wilks approach does not. Thus, our method allows for more robust ML-based analyses critical to performing accurate but computationally feasible global fits. This allows, for the first time, a global fit to sterile neutrino data without assuming Wilks’ theorem. While we demonstrate the utility of such a technique studying sterile neutrino searches, it is applicable to both single-experiment and global fits of all kinds.