Real-time evaluation of laser-driven byproducts is crucial for state-of-the-art facilities operating at high repetition rates. This work presents real-time measurements of hard X-rays (bremsstrahlung radiation) generated from the interaction of high-intensity laser pulses with solid targets in the target normal sheath acceleration regime using a scintillator stack detector. The detector offers insights into the effectiveness of laser–plasma interaction through measured fluctuations in bremsstrahlung radiation temperature and scintillation light yield on a shot-to-shot basis. Moreover, a strong correlation of the bremsstrahlung measurements (i.e., temperature and yield) with the cutoff energy of laser-driven protons was observed. The scintillator stack detector serves not only as a diagnostic for online monitoring of the laser–plasma interaction but also as a promising tool for estimating proton energy fluctuations in a non-disruptive manner, which is particularly important when direct proton source characterization is impractical, for example, during experiments aimed at irradiating user samples with the accelerated proton beam.