Short, intense laser pulses can be used to access the transition regime between classical and quantum optical responses in dielectrics. In this regime, the relative roles of inter- and intraband light-driven electronic transitions remain uncertain. We applied attosecond transient absorption spectroscopy to investigate the interaction between polycrystalline diamond and a few-femtosecond infrared pulse with intensity below the critical intensity of optical breakdown. Ab initio time-dependent density functional theory calculations, in tandem with a two-band parabolic model, accounted for the experimental results in the framework of the dynamical Franz-Keldysh effect and identified infrared induction of intraband currents as the main physical mechanism responsible for the observations.