We show that time-domain analysis of high harmonic generation from solids with subcycle resolution and broad, continuous spectral coverage is now experimentally viable due to the emergence of sensitive, solid-state optical-field-sampling techniques. With this experimental opportunity in mind, we use time-dependent density functional theory to explore what insights such a time-domain, field-resolved analysis might uncover about the extreme nonlinear electron dynamics responsible for high-harmonic generation (HHG) within solids. We illustrate how simple, visual analysis of the time-domain fields provides clear insight into the interplay between intra- and interband dynamical processes underlying nonlinear light generation when spectral signatures do not. Importantly, we observe conditions where the dominant emission mechanism suddenly switches from intra- to interband over a subcycle region of time within the pulse envelope of the driving wave form. This complex field response means that phase-resolved techniques requiring a certain level of periodicity are, in general, inadequate for the study of HHG from solids. We find that field-resolved measurements having both subcycle time resolution and broad, nearly continuous spectral coverage are required for a general understanding of solid-state HHG.