We report on an improved microwave detection protocol for dark matter candidates such as the axion and the dark photon. We employ a superconducting transmon qubit dispersively coupled to a double-cavity system, enabling quantum non-demolition measurements of the photon occupation in a relatively short-lived storage cavity. To reduce the experimental cycle time and enhance sensitivity for axion and dark-photon searches, we operate this detector in a regime of increased qubit–cavity coupling, resulting in Stark shifts of 4.6 MHz. In this regime, conventional control pulses suffer from strong frequency-detuning sensitivity and photon-number–dependent errors. We address this limitation by implementing frequency-detuning–robust $\pi /2$ pulses (obtained by machine- learning optimization) that preserve high-fidelity qubit control over a bandwidth of approximately 20 MHz. We experimentally validate this protocol and demonstrate single-photon detection performance comparable to previous implementations, despite significantly reduced qubit coherence times and storage-cavity lifetimes. Using parity-based measurement sequences combined with a Hidden Markov Model (HMM) analysis, we achieve background rates on the order of $𝒪(20)$~Hz. In the absence of a magnetic field, we derive exclusion limits on the dark photon model for dark matter, reaching a sensitivity to the kinetic mixing angle of ${ϵ}_{95\%}\sim 1\times {10}^{-14}$ at 5.051 GHz. These results establish machine-learning robust control as a key enabler for faster, more scalable microwave quantum sensors for dark-matter searches.