We present a method of constraining the properties of the γ-ray emitting region in flat spectrum radio quasars in the one-zone proton synchrotron model, where the γ-rays are produced by synchrotron radiation of relativistic protons. We show that for low enough values of the Doppler factor δ, the emission from the electromagnetic (EM) cascade which is initiated by the internal absorption of high-energy photons from photohadronic interactions may exceed the observed ∼GeV flux. We use that effect to derive an absolute lower limit of δ; first, an analytical one, in the asymptotic limit where the external radiation from the broad-line region (BLR) is negligible, and then a numerical one in the more general case that includes BLR radiation. As its energy density in the emission region depends on δ and the region's distance from the galactic centre, we use the EM cascade to determine a minimum distance for each value of δ. We complement the EM cascade constraint with one derived from variability arguments and apply our method to the FSRQ 3C 273. We find that δ ≳ 18-20 for B ≲ 30 G and ∼day time-scale variability; the emission region is located outside the BLR, namely at r ≳ 10RBLR ∼ 3 pc; the model requires at pc-scale distances stronger magnetic fields than those inferred from core shift observations; while the jet power exceeds by at least one order of magnitude the accretion power. In short, our results disfavour the proton synchrotron model for the FSRQ 3C 273.