Obtaining a combination of high toughness and strength is crucial for most structural materials, but unfortunately these tend to be mutually exclusive. The search for strong and tough damage-resistant materials has thus typically been based on achieving an acceptable compromise between hardness and crack resistance. Focusing here on brittle oxide glasses, we propose a new strategy for overcoming this conflict by identifying new structural motifs for designing hard and crack-resistant glasses. Specifically, we report that surprisingly there is no decrease in the densification contribution to deformation of a mixed network ${\mathrm{Al}}_2{O}_3-B_2{O}_3-P_2{O}_5-\mathrm{Si}{O}_2$ bulk glass following predensification of the glass at elevated temperature. Hitherto unique to this glass composition, the treatment reduces the residual stress during subsequent sharp contact loading, which in turn leads to a simultaneous increase in hardness and crack resistance. Based on structural characterization, we show that the more densified medium-range order of the hot compressed glass results in formation of certain structural states (e.g., nonring trigonal boron), which could not be reached through any composition or thermal path. This work thus shows that accessing such “forbidden” structural states through the identified densification at elevated temperatures offers a way forward to overcome the conflict of strength versus toughness in structural materials.