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We investigate nonequilibrium electron dynamics in crystalline ZnO induced by ultrashort, relatively intense, infrared laser pulses. Our focus is on understanding the mechanism that facilitates efficient conduction band population in ZnO to enable optically pumped lasing. We consider two different pulse frequencies (in the near infrared and mid infrared) for which experimental data are available, and we calculate the electronic response of a ZnO crystal for a wide range of pulse intensities. We apply and compare three complementary theoretical approaches: the analytical Keldysh model, the numerical solution of the semiconductor Bloch equations, and real-time time-dependent density functional theory. We conclude that time-dependent density functional theory is a valid ab initio approach for predicting conduction band population, that offers an accurate enough description of static and transient optical properties of solids and provides physics insight into the intermediate excitation regime, where electronic excitations are determined by the interplay of intraband tunneling, a consequence of band bending, and interband multiphoton absorption.