Modern free-electron lasers (FEL) operating in XUV (extreme ultraviolet) or X-ray range allow an access to novel research areas. An example is the ultrafast ionization of a solid by an intense femtosecond FEL pulse in XUV which consequently leads to a change of the complex index of refraction on an ultrashort timescale. The photoionization and subsequent impact ionization resulting in electronic and atomic dynamics are modeled with our hybrid code XTANT(X-ray thermal and non-thermal transitions) and a Monte Carlo code XCASCADE(X-ray-induced electron cascades). The simulations predict the temporal kinetics of FEL-induced electron cascades and thus yield temporally and spatially resolved information on the induced changes of the optical properties. In a series of experiments at FERMI and LCLS, single shot measurements with spatio-temporal encoding of the ionization process have been performed by a correlation of the FEL pump pulse with an optical femtosecond probe pulse. An excellent agreement between the experiment and the simulation has been found. We also show that such kind of experiments forms the basis for pulse duration and arrival time jitter monitoring as currently under development for XUV-FELs.