## 2 Materials and Methods
### Volume Integration of Diffraction Signal  
The structural response of the sample was monitored by the measured strength of the Si (333) Bragg reflection of the probe pulse. It was initially claimed (see [12]) that the peak intensity started to decrease only after 150 \(\pm\) 40 fs. This delayed onset was originally explained in [12] as due to the time needed to complete secondary electron cascading [33; 40] and to achieve electron thermalization. Such thermalization should precede a structural transformation of the irradiated material. However, as the spatial profile of the pump and probe pulse was non-uniform in this experiment, various regions of the crystal experienced different X-ray fluences during the pump pulse depending on their distance to the beam focus. The amplitude of the diffracted probe pulse summed up coherent contributions from various crystal subunits that were differently affected by the beam. Therefore, the experiment recorded a volume integrated signal (i.e., the absolute square of the amplitude), combining the contributions from crystal regions with various absorbed doses. For the calculation of the scattered X-ray intensity, we used the code XSINC [29]. This takes into account a spatially non-uniform profile (approximated to be Gaussian) of the X-ray pump and probe pulses. The X-ray probed region in the bulk crystal is divided into smaller crystal subunits. Their size is kept small so that a uniform pulse fluence can be assumed in each subunit. Various subunits experience different X-ray fluences during the pump pulse, depending on their distance to the beam focus. The pump-pulse-induced atomic dynamics in each subunit are calculated with the code XTANT, which delivers information on the actual atomic positions and electron density at each time step. Five dynamic realizations are calculated for each fluence point. For each crystal subunit, a realization of the XTANT simulated dynamics was chosen randomly. The respective contribution of the subunit to the amplitude of the diffracted probe pulse was then calculated. The amplitude of the diffracted probe pulse was a coherent sum of the contributions from all subunits. In this way, the volume-integrated diffraction signal (i.e., the absolute square of the amplitude) from the entire X-ray-probed region was calculated. Eleven fluence points, covering the range of 0 to 100% of the maximal fluence with 10% steps, were used for constructing the volume-integrated signal. Let us emphasize that this volume integration takes into account only the inhomogeneity of the irradiation in the plane \((x,y)\) lateral to the X-ray beam, and not in the material depth. However, as the beam intensity is exponentially absorbed in the material, the actual dose of the pump pulse absorbed in the material at \((x,y)\) changes with the depth, \(z\) in the material. We neglect this inhomogeneity in \(z\), assuming a uniform absorbed dose for the pump pulse equal to the difference between the surface dose at \(z=0\) and the dose at the material depth corresponding to the X-ray penetration depth. This yields the \((1-1/e)\) fraction of the surface dose at \((x,y)\). The justification is the following: the cross section for the elastic scattering of X-rays in Si for the photon wavelength of 5.95 keV is only a very small fraction (0.7%) of the total X-ray scattering cross section [41]. This implies that the intensity of the elastically scattered coherent X-rays is only a minor fraction of the incoming X-ray intensity of the probe pulse. As these incoming X-rays are strongly absorbed in the material, the actual fraction of the Bragg-scattered X-ray signal will be exponentially attenuated with the increasing \(z\). In addition, the coherently scattered signal will also be exponentially attenuated while passing through the crystal toward the detector.