Recent studies confirmed that the materials used in the extreme UV and soft X-ray regime for precise characterization of intense free-electron laser pulses (e.g., Si3N4) do not work efficiently in the hard X-ray regime, which is due to the fact that the impact of a hard X-ray photon is followed by a series of electron cascading processes. Following theoretical indication, we show that this limitation can be circumvented and the cascading time can be significantly reduced if the X-ray photon energy is double the ionization energy. We investigate an alternative material for pulse diagnostics, SnO2, using the Linac Coherent Light Source at photon energies of 5 keV and 9 keV. We prove the validity of the concept and show that it has a large potential for practical applications. By applying the proposed criteria, the temporal accuracy of the non-invasive pulse diagnostic tools can be improved in current and emerging hard X-ray facilities.